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Present Your Data Like a Pro

• Joel Schwartzberg

Demystify the numbers. Your audience will thank you.

While a good presentation has data, data alone doesn’t guarantee a good presentation. It’s all about how that data is presented. The quickest way to confuse your audience is by sharing too many details at once. The only data points you should share are those that significantly support your point — and ideally, one point per chart. To avoid the debacle of sheepishly translating hard-to-see numbers and labels, rehearse your presentation with colleagues sitting as far away as the actual audience would. While you’ve been working with the same chart for weeks or months, your audience will be exposed to it for mere seconds. Give them the best chance of comprehending your data by using simple, clear, and complete language to identify X and Y axes, pie pieces, bars, and other diagrammatic elements. Try to avoid abbreviations that aren’t obvious, and don’t assume labeled components on one slide will be remembered on subsequent slides. Every valuable chart or pie graph has an “Aha!” zone — a number or range of data that reveals something crucial to your point. Make sure you visually highlight the “Aha!” zone, reinforcing the moment by explaining it to your audience.

With so many ways to spin and distort information these days, a presentation needs to do more than simply share great ideas — it needs to support those ideas with credible data. That’s true whether you’re an executive pitching new business clients, a vendor selling her services, or a CEO making a case for change.

• JS Joel Schwartzberg oversees executive communications for a major national nonprofit, is a professional presentation coach, and is the author of Get to the Point! Sharpen Your Message and Make Your Words Matter and The Language of Leadership: How to Engage and Inspire Your Team . You can find him on LinkedIn and X. TheJoelTruth

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Home Blog Design Understanding Data Presentations (Guide + Examples)

Understanding Data Presentations (Guide + Examples)

In this age of overwhelming information, the skill to effectively convey data has become extremely valuable. Initiating a discussion on data presentation types involves thoughtful consideration of the nature of your data and the message you aim to convey. Different types of visualizations serve distinct purposes. Whether you’re dealing with how to develop a report or simply trying to communicate complex information, how you present data influences how well your audience understands and engages with it. This extensive guide leads you through the different ways of data presentation.

Table of Contents

What is a Data Presentation?

What should a data presentation include, line graphs, treemap chart, scatter plot, how to choose a data presentation type, recommended data presentation templates, common mistakes done in data presentation.

A data presentation is a slide deck that aims to disclose quantitative information to an audience through the use of visual formats and narrative techniques derived from data analysis, making complex data understandable and actionable. This process requires a series of tools, such as charts, graphs, tables, infographics, dashboards, and so on, supported by concise textual explanations to improve understanding and boost retention rate.

Data presentations require us to cull data in a format that allows the presenter to highlight trends, patterns, and insights so that the audience can act upon the shared information. In a few words, the goal of data presentations is to enable viewers to grasp complicated concepts or trends quickly, facilitating informed decision-making or deeper analysis.

Data presentations go beyond the mere usage of graphical elements. Seasoned presenters encompass visuals with the art of data storytelling , so the speech skillfully connects the points through a narrative that resonates with the audience. Depending on the purpose – inspire, persuade, inform, support decision-making processes, etc. – is the data presentation format that is better suited to help us in this journey.

To nail your upcoming data presentation, ensure to count with the following elements:

• Clear Objectives: Understand the intent of your presentation before selecting the graphical layout and metaphors to make content easier to grasp.
• Engaging introduction: Use a powerful hook from the get-go. For instance, you can ask a big question or present a problem that your data will answer. Take a look at our guide on how to start a presentation for tips & insights.
• Structured Narrative: Your data presentation must tell a coherent story. This means a beginning where you present the context, a middle section in which you present the data, and an ending that uses a call-to-action. Check our guide on presentation structure for further information.
• Visual Elements: These are the charts, graphs, and other elements of visual communication we ought to use to present data. This article will cover one by one the different types of data representation methods we can use, and provide further guidance on choosing between them.
• Insights and Analysis: This is not just showcasing a graph and letting people get an idea about it. A proper data presentation includes the interpretation of that data, the reason why it’s included, and why it matters to your research.
• Conclusion & CTA: Ending your presentation with a call to action is necessary. Whether you intend to wow your audience into acquiring your services, inspire them to change the world, or whatever the purpose of your presentation, there must be a stage in which you convey all that you shared and show the path to staying in touch. Plan ahead whether you want to use a thank-you slide, a video presentation, or which method is apt and tailored to the kind of presentation you deliver.
• Q&A Session: After your speech is concluded, allocate 3-5 minutes for the audience to raise any questions about the information you disclosed. This is an extra chance to establish your authority on the topic. Check our guide on questions and answer sessions in presentations here.

Bar charts are a graphical representation of data using rectangular bars to show quantities or frequencies in an established category. They make it easy for readers to spot patterns or trends. Bar charts can be horizontal or vertical, although the vertical format is commonly known as a column chart. They display categorical, discrete, or continuous variables grouped in class intervals [1] . They include an axis and a set of labeled bars horizontally or vertically. These bars represent the frequencies of variable values or the values themselves. Numbers on the y-axis of a vertical bar chart or the x-axis of a horizontal bar chart are called the scale.

Real-Life Application of Bar Charts

Let’s say a sales manager is presenting sales to their audience. Using a bar chart, he follows these steps.

Step 1: Selecting Data

The first step is to identify the specific data you will present to your audience.

The sales manager has highlighted these products for the presentation.

• Product A: Men’s Shoes
• Product B: Women’s Apparel
• Product C: Electronics
• Product D: Home Decor

Step 2: Choosing Orientation

Opt for a vertical layout for simplicity. Vertical bar charts help compare different categories in case there are not too many categories [1] . They can also help show different trends. A vertical bar chart is used where each bar represents one of the four chosen products. After plotting the data, it is seen that the height of each bar directly represents the sales performance of the respective product.

It is visible that the tallest bar (Electronics – Product C) is showing the highest sales. However, the shorter bars (Women’s Apparel – Product B and Home Decor – Product D) need attention. It indicates areas that require further analysis or strategies for improvement.

Step 3: Colorful Insights

Different colors are used to differentiate each product. It is essential to show a color-coded chart where the audience can distinguish between products.

• Men’s Shoes (Product A): Yellow
• Women’s Apparel (Product B): Orange
• Electronics (Product C): Violet
• Home Decor (Product D): Blue

Bar charts are straightforward and easily understandable for presenting data. They are versatile when comparing products or any categorical data [2] . Bar charts adapt seamlessly to retail scenarios. Despite that, bar charts have a few shortcomings. They cannot illustrate data trends over time. Besides, overloading the chart with numerous products can lead to visual clutter, diminishing its effectiveness.

For more information, check our collection of bar chart templates for PowerPoint .

Line graphs help illustrate data trends, progressions, or fluctuations by connecting a series of data points called ‘markers’ with straight line segments. This provides a straightforward representation of how values change [5] . Their versatility makes them invaluable for scenarios requiring a visual understanding of continuous data. In addition, line graphs are also useful for comparing multiple datasets over the same timeline. Using multiple line graphs allows us to compare more than one data set. They simplify complex information so the audience can quickly grasp the ups and downs of values. From tracking stock prices to analyzing experimental results, you can use line graphs to show how data changes over a continuous timeline. They show trends with simplicity and clarity.

Real-life Application of Line Graphs

To understand line graphs thoroughly, we will use a real case. Imagine you’re a financial analyst presenting a tech company’s monthly sales for a licensed product over the past year. Investors want insights into sales behavior by month, how market trends may have influenced sales performance and reception to the new pricing strategy. To present data via a line graph, you will complete these steps.

First, you need to gather the data. In this case, your data will be the sales numbers. For example:

• January: $45,000
• February: $55,000
• March: $45,000
• April: $60,000
• May: $ 70,000
• June: $65,000
• July: $62,000
• August: $68,000
• September: $81,000
• October: $76,000
• November: $87,000
• December: $91,000

After choosing the data, the next step is to select the orientation. Like bar charts, you can use vertical or horizontal line graphs. However, we want to keep this simple, so we will keep the timeline (x-axis) horizontal while the sales numbers (y-axis) vertical.

Step 3: Connecting Trends

After adding the data to your preferred software, you will plot a line graph. In the graph, each month’s sales are represented by data points connected by a line.

Step 4: Adding Clarity with Color

If there are multiple lines, you can also add colors to highlight each one, making it easier to follow.

Line graphs excel at visually presenting trends over time. These presentation aids identify patterns, like upward or downward trends. However, too many data points can clutter the graph, making it harder to interpret. Line graphs work best with continuous data but are not suitable for categories.

For more information, check our collection of line chart templates for PowerPoint and our article about how to make a presentation graph .

A data dashboard is a visual tool for analyzing information. Different graphs, charts, and tables are consolidated in a layout to showcase the information required to achieve one or more objectives. Dashboards help quickly see Key Performance Indicators (KPIs). You don’t make new visuals in the dashboard; instead, you use it to display visuals you’ve already made in worksheets [3] .

Keeping the number of visuals on a dashboard to three or four is recommended. Adding too many can make it hard to see the main points [4]. Dashboards can be used for business analytics to analyze sales, revenue, and marketing metrics at a time. They are also used in the manufacturing industry, as they allow users to grasp the entire production scenario at the moment while tracking the core KPIs for each line.

Real-Life Application of a Dashboard

Consider a project manager presenting a software development project’s progress to a tech company’s leadership team. He follows the following steps.

Step 1: Defining Key Metrics

To effectively communicate the project’s status, identify key metrics such as completion status, budget, and bug resolution rates. Then, choose measurable metrics aligned with project objectives.

Step 2: Choosing Visualization Widgets

After finalizing the data, presentation aids that align with each metric are selected. For this project, the project manager chooses a progress bar for the completion status and uses bar charts for budget allocation. Likewise, he implements line charts for bug resolution rates.

Step 3: Dashboard Layout

Key metrics are prominently placed in the dashboard for easy visibility, and the manager ensures that it appears clean and organized.

Dashboards provide a comprehensive view of key project metrics. Users can interact with data, customize views, and drill down for detailed analysis. However, creating an effective dashboard requires careful planning to avoid clutter. Besides, dashboards rely on the availability and accuracy of underlying data sources.

For more information, check our article on how to design a dashboard presentation , and discover our collection of dashboard PowerPoint templates .

Treemap charts represent hierarchical data structured in a series of nested rectangles [6] . As each branch of the ‘tree’ is given a rectangle, smaller tiles can be seen representing sub-branches, meaning elements on a lower hierarchical level than the parent rectangle. Each one of those rectangular nodes is built by representing an area proportional to the specified data dimension.

Treemaps are useful for visualizing large datasets in compact space. It is easy to identify patterns, such as which categories are dominant. Common applications of the treemap chart are seen in the IT industry, such as resource allocation, disk space management, website analytics, etc. Also, they can be used in multiple industries like healthcare data analysis, market share across different product categories, or even in finance to visualize portfolios.

Real-Life Application of a Treemap Chart

Let’s consider a financial scenario where a financial team wants to represent the budget allocation of a company. There is a hierarchy in the process, so it is helpful to use a treemap chart. In the chart, the top-level rectangle could represent the total budget, and it would be subdivided into smaller rectangles, each denoting a specific department. Further subdivisions within these smaller rectangles might represent individual projects or cost categories.

Step 1: Define Your Data Hierarchy

While presenting data on the budget allocation, start by outlining the hierarchical structure. The sequence will be like the overall budget at the top, followed by departments, projects within each department, and finally, individual cost categories for each project.

• Top-level rectangle: Total Budget
• Second-level rectangles: Departments (Engineering, Marketing, Sales)
• Third-level rectangles: Projects within each department
• Fourth-level rectangles: Cost categories for each project (Personnel, Marketing Expenses, Equipment)

Step 2: Choose a Suitable Tool

It’s time to select a data visualization tool supporting Treemaps. Popular choices include Tableau, Microsoft Power BI, PowerPoint, or even coding with libraries like D3.js. It is vital to ensure that the chosen tool provides customization options for colors, labels, and hierarchical structures.

Here, the team uses PowerPoint for this guide because of its user-friendly interface and robust Treemap capabilities.

Step 3: Make a Treemap Chart with PowerPoint

After opening the PowerPoint presentation, they chose “SmartArt” to form the chart. The SmartArt Graphic window has a “Hierarchy” category on the left.  Here, you will see multiple options. You can choose any layout that resembles a Treemap. The “Table Hierarchy” or “Organization Chart” options can be adapted. The team selects the Table Hierarchy as it looks close to a Treemap.

Step 5: Input Your Data

After that, a new window will open with a basic structure. They add the data one by one by clicking on the text boxes. They start with the top-level rectangle, representing the total budget.  

Step 6: Customize the Treemap

By clicking on each shape, they customize its color, size, and label. At the same time, they can adjust the font size, style, and color of labels by using the options in the “Format” tab in PowerPoint. Using different colors for each level enhances the visual difference.

Treemaps excel at illustrating hierarchical structures. These charts make it easy to understand relationships and dependencies. They efficiently use space, compactly displaying a large amount of data, reducing the need for excessive scrolling or navigation. Additionally, using colors enhances the understanding of data by representing different variables or categories.

In some cases, treemaps might become complex, especially with deep hierarchies.  It becomes challenging for some users to interpret the chart. At the same time, displaying detailed information within each rectangle might be constrained by space. It potentially limits the amount of data that can be shown clearly. Without proper labeling and color coding, there’s a risk of misinterpretation.

A heatmap is a data visualization tool that uses color coding to represent values across a two-dimensional surface. In these, colors replace numbers to indicate the magnitude of each cell. This color-shaded matrix display is valuable for summarizing and understanding data sets with a glance [7] . The intensity of the color corresponds to the value it represents, making it easy to identify patterns, trends, and variations in the data.

As a tool, heatmaps help businesses analyze website interactions, revealing user behavior patterns and preferences to enhance overall user experience. In addition, companies use heatmaps to assess content engagement, identifying popular sections and areas of improvement for more effective communication. They excel at highlighting patterns and trends in large datasets, making it easy to identify areas of interest.

We can implement heatmaps to express multiple data types, such as numerical values, percentages, or even categorical data. Heatmaps help us easily spot areas with lots of activity, making them helpful in figuring out clusters [8] . When making these maps, it is important to pick colors carefully. The colors need to show the differences between groups or levels of something. And it is good to use colors that people with colorblindness can easily see.

Check our detailed guide on how to create a heatmap here. Also discover our collection of heatmap PowerPoint templates .

Pie charts are circular statistical graphics divided into slices to illustrate numerical proportions. Each slice represents a proportionate part of the whole, making it easy to visualize the contribution of each component to the total.

The size of the pie charts is influenced by the value of data points within each pie. The total of all data points in a pie determines its size. The pie with the highest data points appears as the largest, whereas the others are proportionally smaller. However, you can present all pies of the same size if proportional representation is not required [9] . Sometimes, pie charts are difficult to read, or additional information is required. A variation of this tool can be used instead, known as the donut chart , which has the same structure but a blank center, creating a ring shape. Presenters can add extra information, and the ring shape helps to declutter the graph.

Pie charts are used in business to show percentage distribution, compare relative sizes of categories, or present straightforward data sets where visualizing ratios is essential.

Real-Life Application of Pie Charts

Consider a scenario where you want to represent the distribution of the data. Each slice of the pie chart would represent a different category, and the size of each slice would indicate the percentage of the total portion allocated to that category.

Step 1: Define Your Data Structure

Imagine you are presenting the distribution of a project budget among different expense categories.

• Column A: Expense Categories (Personnel, Equipment, Marketing, Miscellaneous)
• Column B: Budget Amounts ($40,000, $30,000, $20,000, $10,000) Column B represents the values of your categories in Column A.

Step 2: Insert a Pie Chart

Using any of the accessible tools, you can create a pie chart. The most convenient tools for forming a pie chart in a presentation are presentation tools such as PowerPoint or Google Slides.  You will notice that the pie chart assigns each expense category a percentage of the total budget by dividing it by the total budget.

For instance:

• Personnel: $40,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 40%
• Equipment: $30,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 30%
• Marketing: $20,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 20%
• Miscellaneous: $10,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 10%

You can make a chart out of this or just pull out the pie chart from the data.

3D pie charts and 3D donut charts are quite popular among the audience. They stand out as visual elements in any presentation slide, so let’s take a look at how our pie chart example would look in 3D pie chart format.

Step 03: Results Interpretation

The pie chart visually illustrates the distribution of the project budget among different expense categories. Personnel constitutes the largest portion at 40%, followed by equipment at 30%, marketing at 20%, and miscellaneous at 10%. This breakdown provides a clear overview of where the project funds are allocated, which helps in informed decision-making and resource management. It is evident that personnel are a significant investment, emphasizing their importance in the overall project budget.

Pie charts provide a straightforward way to represent proportions and percentages. They are easy to understand, even for individuals with limited data analysis experience. These charts work well for small datasets with a limited number of categories.

However, a pie chart can become cluttered and less effective in situations with many categories. Accurate interpretation may be challenging, especially when dealing with slight differences in slice sizes. In addition, these charts are static and do not effectively convey trends over time.

For more information, check our collection of pie chart templates for PowerPoint .

Histograms present the distribution of numerical variables. Unlike a bar chart that records each unique response separately, histograms organize numeric responses into bins and show the frequency of reactions within each bin [10] . The x-axis of a histogram shows the range of values for a numeric variable. At the same time, the y-axis indicates the relative frequencies (percentage of the total counts) for that range of values.

Whenever you want to understand the distribution of your data, check which values are more common, or identify outliers, histograms are your go-to. Think of them as a spotlight on the story your data is telling. A histogram can provide a quick and insightful overview if you’re curious about exam scores, sales figures, or any numerical data distribution.

Real-Life Application of a Histogram

In the histogram data analysis presentation example, imagine an instructor analyzing a class’s grades to identify the most common score range. A histogram could effectively display the distribution. It will show whether most students scored in the average range or if there are significant outliers.

Step 1: Gather Data

He begins by gathering the data. The scores of each student in class are gathered to analyze exam scores.

After arranging the scores in ascending order, bin ranges are set.

Step 2: Define Bins

Bins are like categories that group similar values. Think of them as buckets that organize your data. The presenter decides how wide each bin should be based on the range of the values. For instance, the instructor sets the bin ranges based on score intervals: 60-69, 70-79, 80-89, and 90-100.

Step 3: Count Frequency

Now, he counts how many data points fall into each bin. This step is crucial because it tells you how often specific ranges of values occur. The result is the frequency distribution, showing the occurrences of each group.

Here, the instructor counts the number of students in each category.

• 60-69: 1 student (Kate)
• 70-79: 4 students (David, Emma, Grace, Jack)
• 80-89: 7 students (Alice, Bob, Frank, Isabel, Liam, Mia, Noah)
• 90-100: 3 students (Clara, Henry, Olivia)

Step 4: Create the Histogram

It’s time to turn the data into a visual representation. Draw a bar for each bin on a graph. The width of the bar should correspond to the range of the bin, and the height should correspond to the frequency.  To make your histogram understandable, label the X and Y axes.

In this case, the X-axis should represent the bins (e.g., test score ranges), and the Y-axis represents the frequency.

The histogram of the class grades reveals insightful patterns in the distribution. Most students, with seven students, fall within the 80-89 score range. The histogram provides a clear visualization of the class’s performance. It showcases a concentration of grades in the upper-middle range with few outliers at both ends. This analysis helps in understanding the overall academic standing of the class. It also identifies the areas for potential improvement or recognition.

Thus, histograms provide a clear visual representation of data distribution. They are easy to interpret, even for those without a statistical background. They apply to various types of data, including continuous and discrete variables. One weak point is that histograms do not capture detailed patterns in students’ data, with seven compared to other visualization methods.

A scatter plot is a graphical representation of the relationship between two variables. It consists of individual data points on a two-dimensional plane. This plane plots one variable on the x-axis and the other on the y-axis. Each point represents a unique observation. It visualizes patterns, trends, or correlations between the two variables.

Scatter plots are also effective in revealing the strength and direction of relationships. They identify outliers and assess the overall distribution of data points. The points’ dispersion and clustering reflect the relationship’s nature, whether it is positive, negative, or lacks a discernible pattern. In business, scatter plots assess relationships between variables such as marketing cost and sales revenue. They help present data correlations and decision-making.

Real-Life Application of Scatter Plot

A group of scientists is conducting a study on the relationship between daily hours of screen time and sleep quality. After reviewing the data, they managed to create this table to help them build a scatter plot graph:

In the provided example, the x-axis represents Daily Hours of Screen Time, and the y-axis represents the Sleep Quality Rating.

The scientists observe a negative correlation between the amount of screen time and the quality of sleep. This is consistent with their hypothesis that blue light, especially before bedtime, has a significant impact on sleep quality and metabolic processes.

There are a few things to remember when using a scatter plot. Even when a scatter diagram indicates a relationship, it doesn’t mean one variable affects the other. A third factor can influence both variables. The more the plot resembles a straight line, the stronger the relationship is perceived [11] . If it suggests no ties, the observed pattern might be due to random fluctuations in data. When the scatter diagram depicts no correlation, whether the data might be stratified is worth considering.

Choosing the appropriate data presentation type is crucial when making a presentation . Understanding the nature of your data and the message you intend to convey will guide this selection process. For instance, when showcasing quantitative relationships, scatter plots become instrumental in revealing correlations between variables. If the focus is on emphasizing parts of a whole, pie charts offer a concise display of proportions. Histograms, on the other hand, prove valuable for illustrating distributions and frequency patterns. 

Bar charts provide a clear visual comparison of different categories. Likewise, line charts excel in showcasing trends over time, while tables are ideal for detailed data examination. Starting a presentation on data presentation types involves evaluating the specific information you want to communicate and selecting the format that aligns with your message. This ensures clarity and resonance with your audience from the beginning of your presentation.

1. Fact Sheet Dashboard for Data Presentation

Convey all the data you need to present in this one-pager format, an ideal solution tailored for users looking for presentation aids. Global maps, donut chats, column graphs, and text neatly arranged in a clean layout presented in light and dark themes.

Use This Template

2. 3D Column Chart Infographic PPT Template

Represent column charts in a highly visual 3D format with this PPT template. A creative way to present data, this template is entirely editable, and we can craft either a one-page infographic or a series of slides explaining what we intend to disclose point by point.

3. Data Circles Infographic PowerPoint Template

An alternative to the pie chart and donut chart diagrams, this template features a series of curved shapes with bubble callouts as ways of presenting data. Expand the information for each arch in the text placeholder areas.

4. Colorful Metrics Dashboard for Data Presentation

This versatile dashboard template helps us in the presentation of the data by offering several graphs and methods to convert numbers into graphics. Implement it for e-commerce projects, financial projections, project development, and more.

5. Animated Data Presentation Tools for PowerPoint & Google Slides

A slide deck filled with most of the tools mentioned in this article, from bar charts, column charts, treemap graphs, pie charts, histogram, etc. Animated effects make each slide look dynamic when sharing data with stakeholders.

6. Statistics Waffle Charts PPT Template for Data Presentations

This PPT template helps us how to present data beyond the typical pie chart representation. It is widely used for demographics, so it’s a great fit for marketing teams, data science professionals, HR personnel, and more.

7. Data Presentation Dashboard Template for Google Slides

A compendium of tools in dashboard format featuring line graphs, bar charts, column charts, and neatly arranged placeholder text areas. 

8. Weather Dashboard for Data Presentation

Share weather data for agricultural presentation topics, environmental studies, or any kind of presentation that requires a highly visual layout for weather forecasting on a single day. Two color themes are available.

9. Social Media Marketing Dashboard Data Presentation Template

Intended for marketing professionals, this dashboard template for data presentation is a tool for presenting data analytics from social media channels. Two slide layouts featuring line graphs and column charts.

10. Project Management Summary Dashboard Template

A tool crafted for project managers to deliver highly visual reports on a project’s completion, the profits it delivered for the company, and expenses/time required to execute it. 4 different color layouts are available.

11. Profit & Loss Dashboard for PowerPoint and Google Slides

A must-have for finance professionals. This typical profit & loss dashboard includes progress bars, donut charts, column charts, line graphs, and everything that’s required to deliver a comprehensive report about a company’s financial situation.

Overwhelming visuals

One of the mistakes related to using data-presenting methods is including too much data or using overly complex visualizations. They can confuse the audience and dilute the key message.

Inappropriate chart types

Choosing the wrong type of chart for the data at hand can lead to misinterpretation. For example, using a pie chart for data that doesn’t represent parts of a whole is not right.

Lack of context

Failing to provide context or sufficient labeling can make it challenging for the audience to understand the significance of the presented data.

Inconsistency in design

Using inconsistent design elements and color schemes across different visualizations can create confusion and visual disarray.

Failure to provide details

Simply presenting raw data without offering clear insights or takeaways can leave the audience without a meaningful conclusion.

Lack of focus

Not having a clear focus on the key message or main takeaway can result in a presentation that lacks a central theme.

Visual accessibility issues

Overlooking the visual accessibility of charts and graphs can exclude certain audience members who may have difficulty interpreting visual information.

In order to avoid these mistakes in data presentation, presenters can benefit from using presentation templates . These templates provide a structured framework. They ensure consistency, clarity, and an aesthetically pleasing design, enhancing data communication’s overall impact.

Understanding and choosing data presentation types are pivotal in effective communication. Each method serves a unique purpose, so selecting the appropriate one depends on the nature of the data and the message to be conveyed. The diverse array of presentation types offers versatility in visually representing information, from bar charts showing values to pie charts illustrating proportions. 

Using the proper method enhances clarity, engages the audience, and ensures that data sets are not just presented but comprehensively understood. By appreciating the strengths and limitations of different presentation types, communicators can tailor their approach to convey information accurately, developing a deeper connection between data and audience understanding.

[1] Government of Canada, S.C. (2021) 5 Data Visualization 5.2 Bar Chart , 5.2 Bar chart .  https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch9/bargraph-diagrammeabarres/5214818-eng.htm

[2] Kosslyn, S.M., 1989. Understanding charts and graphs. Applied cognitive psychology, 3(3), pp.185-225. https://apps.dtic.mil/sti/pdfs/ADA183409.pdf

[3] Creating a Dashboard . https://it.tufts.edu/book/export/html/1870

[4] https://www.goldenwestcollege.edu/research/data-and-more/data-dashboards/index.html

[5] https://www.mit.edu/course/21/21.guide/grf-line.htm

[6] Jadeja, M. and Shah, K., 2015, January. Tree-Map: A Visualization Tool for Large Data. In GSB@ SIGIR (pp. 9-13). https://ceur-ws.org/Vol-1393/gsb15proceedings.pdf#page=15

[7] Heat Maps and Quilt Plots. https://www.publichealth.columbia.edu/research/population-health-methods/heat-maps-and-quilt-plots

[8] EIU QGIS WORKSHOP. https://www.eiu.edu/qgisworkshop/heatmaps.php

[9] About Pie Charts.  https://www.mit.edu/~mbarker/formula1/f1help/11-ch-c8.htm

[10] Histograms. https://sites.utexas.edu/sos/guided/descriptive/numericaldd/descriptiven2/histogram/ [11] https://asq.org/quality-resources/scatter-diagram

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“Statistics is the grammar of science.” – Karl Pearson

Data and statistics are part of almost every sector and are used to understand and drive results.

These are essential tools to make decisions, answer important questions, summarize big data, recognize patterns, prove theories, etc.

A good presentation gets the backing of data and statistics, but data alone will not guarantee the success of a presentation.

How you choose to present that data either doubles or decimates the impact of your presentation.

While you get weeks working on the charts and numbers, your audience gets only a few minutes to go through the content. So, it becomes all the more imperative that you present it in the most comprehensible way possible for them to understand and remember.

Unfortunately, most of us, at some point, have sat through presentations where the slides didn’t make much sense, and we had to rely on the speaker to know more.

So, take the help of these pointers to turn your complex numbers into interesting information. Let’s begin.

Tips to Deliver Statistics and Analytics in an Impactful Manner

Your presentation might look boring and lengthy if not presented well. Here are some quick tips to make your data lively and impactful.

1. Graphics are the Way to Go

Imagine a slide with a lot of data and numbers presented just like that. How difficult would it be to make sense of it or to read it?

Graphics and visuals are the most powerful way to present numbers. It can make your data easy to understand, livelier, and better accessible to your audience. Graphics and visuals help break down complex and intricate information into readable content.

Keep these tips in mind when using graphics-

Your visuals should not overlap the text and vice versa.

The graphics should be in alignment with your brand and the broader theme of the presentation.

Choose the right graph. For example, a bar graph is apt when you want to compare, and a line graph can be used to depict changes over time.

You can use pre-designed presentation templates featuring relevant graphics and charts to complement your statistical and analytical data and present it in a simple yet trendy way.

Stories and Analogies are Incredibly Powerful

Do you know what mnemonics and memory palaces do? They help you associate the things you want to remember with certain other easy-to-remember things (which you already know).

It took you a lot of time to craft all that information in your presentation, and consider it a bonus if people will remember parts of it later on.

Storytelling is one of the most potent ways to capture attention and aid memory retention. Try to weave a story around the data to help people understand and recollect the data better.

Analogies will help soften the impact of everything technical and non-understandable into something familiar to the audience.

For example, if your presentation is about business growth, you can highlight the increase in numbers with what took you to reach there, i.e., how you improved the website’s visibility, interface, etc.

For more understanding, watch this video displaying a few stunning examples of data storytelling.

3. Highlight Points that Your Data is Illustrating (Inference)

When you present data on the slides , it is not that the numbers hold the real value but the inference drawn from it. Remember to highlight well how the statistics and analytics support your major points.

Don’t leave the decoding part to the audience, or your audience won’t be able to process the relevancy of your argument. When you want to connect the statistic with an inference, make sure the transition is clear with terms such as ‘the numbers show,’ ‘this data proves,’ ‘this figure/chart illustrates,’ etc.

The transitions are critical to bringing everyone’s attention to the most important part of relating to and explaining the conclusions. Not everyone likes to crunch numbers, so highlight the inference in such a way that there is no scope of confusion left for people.

4. Your Data Should be Visible

It sounds obvious, right? But it is a common mistake while placing data on the slides. When you have a lot of information to share, with only so much place on a single slide, it might so happen that some content is aptly visible on a laptop but not so much from a distance in the actual presentation.

To avoid the debacle of having to translate poorly visible numbers and labels, practice your presentation by having people sit as far away as in the actual presentation. Make sure that each slide is clearly visible and readable with all information.

It will also help you align and tweak the material on the slides (keeping only the relevant and required content).

5. Share Only One Piece of Information

When you have a lot of information to share, it becomes an impulse to share everything you know. It is also hard to filter out information that you can exclude from relevant figures. And last, a lot of presenters feel that they are required to share all the information they present - on the slides - as well.

Chaos on the slides with too many details and overuse of the negative space – yes, it will show people the work you have done and the data you have collected, but it will be just that. It will confuse your audience and miss the point for you.

Include data points that significantly support your main argument, and it should be one point on one slide/chart. Enquire yourself what’s the most important learning that you want people to take from that data. Convey that to people.

If you have multiple key points, present each with new visualizations. It will help you demarcate your presentation neatly into understandable chunks and help people remember better. Also, refrain from including unnecessary information that doesn’t directly affect your main point.

6. Use Colors Wisely

Colors will help you differentiate between figures and charts. It can help people figure out the before and after clearly. Presenting the data in black and white wouldn’t be impactful.

Remember to use colors consistently when presenting the same values in a chart . You wouldn’t want your audience confused and draw inaccurate conclusions by highlighting a similar figure in different colors. You can also use brand colors in your presentation to appear more professional.

Another way of using the colors in a user-friendly way is by matching the axis and series colors when you are presenting a dual-axis chart. It will help your audience match the series with the respective axis easily. There are a lot of other ways in which you can use colors to bring coherency and life to your data.

7. You can Present the Data in Stages

Animating your charts will make the data look less intimidating and help people derive more information from the figures. Presenting your data in stages will enhance comprehension and give everyone time to process it properly.

For example, let’s say you are showing the sale of 2 products. You can show the chart in 3 stages by explaining the axes in one, then a chart for the sale of product X as a base (2nd stage), and after that for product Y (3rd stage).

PowerPoint has a chart animation feature that lets you do it by series or category.

The technique will aid you in presenting your data effectively and efficiently.

8. Go Simple

Don’t scare your audience with a barrage of numbers. You have had time to soak in everything you want to tell, but this won’t be the case with people sitting in front. Try to be simple with the data you are presenting. For instance, keep the format of your number simple. Don’t make people count the number of zeroes like 10000 vs. 1000000.

Try to include decimals (skip unnecessary decimals) for numbers that are close to each other in a range of values and not for numbers as far away as 2-90%. If your numbers are within a few percent range of each other, it is important to use decimals.

Another factor that can help simplify your data is keeping the numbers right-aligned always. It can help people scan the numbers (to study), which becomes a little harder in the case of center-aligned numbers.

9. Initiate with the End

Try to start by giving the bottom line up front. Let us explain what it means. Your audience will naturally scan your slide from top to bottom. Your titles should give a clear picture of your chart. Rather than going for vague titles and letting people fumble through the slides to figure out the key message – share a clear title that will immediately let them know what to look for in the slide.

For example, let’s say your chart is about a certain product’s growth over other products. Go for a title that says Product C’s growth over the last quarter. Your audience will automatically start scanning the relevant figures related to this product and save time and effort.

Your slide title should be point specific and reinforce the main point. Try not to go for generic words and phrases serving no functional purpose.

10. Remember to Present to the Audience

One mistake that you can make while presenting statistics and analytics is focusing too much on your slides. After all, even you wouldn’t remember all the figures.

It can be detrimental for you as a presenter, as you would not be able to connect to your audience and might look uncompetitive. Therefore, try to keep your gaze on the audience, for they will be able to understand better when you speak while maintaining eye contact.

You can keep cue cards for your reference and look at your slides here and there while emphasizing a point to the audience.

In a Nutshell

Incorporating data and statistics to add credibility to a presentation is a common practice. And finding relevant data is not difficult either. However, how you choose to present that data will define the impact of your presentation.

Keep these above tips in mind to make your figures speak to the audience efficiently.

They will make your presentation appear crisp and appealing and bring life to your statistics and analysis.

Also, remember your presentation should have a clear take-home message. People should know what they are supposed to do with what you have shared. You can include a clear CTA in your presentation to guide everyone better.

About the Author

Ashish Arora is Co-Founder of SketchBubble, a leading provider of result-driven, professionally built PowerPoint templates .

Travelling the world to gather new creative ideas, he has been working in the digital marketing space since 2007 and has a passion for designing presentations.

Continue to: Presenting Data Top Tips for Effective Presentations

See also: Statistical Analysis: Understanding Statistical Distributions Industries Where Employers Value Data Analytics Skills 7 Things That Can Help You Improve Your Data Collection Skills

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statistics , the science of collecting, analyzing, presenting, and interpreting data . Governmental needs for census data as well as information about a variety of economic activities provided much of the early impetus for the field of statistics. Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and practical developments in statistics.

Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation. Data may be classified as either quantitative or qualitative. Quantitative data measure either how much or how many of something, and qualitative data provide labels, or names, for categories of like items. For example, suppose that a particular study is interested in characteristics such as age, gender, marital status, and annual income for a sample of 100 individuals. These characteristics would be called the variables of the study , and data values for each of the variables would be associated with each individual. Thus, the data values of 28, male, single, and $30,000 would be recorded for a 28-year-old single male with an annual income of $30,000. With 100 individuals and 4 variables, the data set would have 100 × 4 = 400 items. In this example, age and annual income are quantitative variables; the corresponding data values indicate how many years and how much money for each individual. Gender and marital status are qualitative variables. The labels male and female provide the qualitative data for gender, and the labels single, married, divorced, and widowed indicate marital status.

Sample survey methods are used to collect data from observational studies, and experimental design methods are used to collect data from experimental studies. The area of descriptive statistics is concerned primarily with methods of presenting and interpreting data using graphs, tables, and numerical summaries. Whenever statisticians use data from a sample—i.e., a subset of the population—to make statements about a population, they are performing statistical inference . Estimation and hypothesis testing are procedures used to make statistical inferences . Fields such as health care, biology , chemistry , physics , education, engineering , business, and economics make extensive use of statistical inference .

Methods of probability were developed initially for the analysis of gambling games. Probability plays a key role in statistical inference; it is used to provide measures of the quality and precision of the inferences. Many of the methods of statistical inference are described in this article. Some of these methods are used primarily for single-variable studies, while others, such as regression and correlation analysis, are used to make inferences about relationships among two or more variables.

Descriptive statistics

Descriptive statistics are tabular, graphical, and numerical summaries of data. The purpose of descriptive statistics is to facilitate the presentation and interpretation of data. Most of the statistical presentations appearing in newspapers and magazines are descriptive in nature. Univariate methods of descriptive statistics use data to enhance the understanding of a single variable; multivariate methods focus on using statistics to understand the relationships among two or more variables. To illustrate methods of descriptive statistics, the previous example in which data were collected on the age, gender, marital status, and annual income of 100 individuals will be examined.

The most commonly used tabular summary of data for a single variable is a frequency distribution . A frequency distribution shows the number of data values in each of several nonoverlapping classes. Another tabular summary, called a relative frequency distribution, shows the fraction, or percentage , of data values in each class. The most common tabular summary of data for two variables is a cross tabulation, a two-variable analogue of a frequency distribution.

For a qualitative variable, a frequency distribution shows the number of data values in each qualitative category. For instance, the variable gender has two categories: male and female. Thus, a frequency distribution for gender would have two nonoverlapping classes to show the number of males and females. A relative frequency distribution for this variable would show the fraction of individuals that are male and the fraction of individuals that are female.

Constructing a frequency distribution for a quantitative variable requires more care in defining the classes and the division points between adjacent classes. For instance, if the age data of the example above ranged from 22 to 78 years, the following six nonoverlapping classes could be used: 20–29, 30–39, 40–49, 50–59, 60–69, and 70–79. A frequency distribution would show the number of data values in each of these classes, and a relative frequency distribution would show the fraction of data values in each.

A cross tabulation is a two-way table with the rows of the table representing the classes of one variable and the columns of the table representing the classes of another variable. To construct a cross tabulation using the variables gender and age, gender could be shown with two rows, male and female, and age could be shown with six columns corresponding to the age classes 20–29, 30–39, 40–49, 50–59, 60–69, and 70–79. The entry in each cell of the table would specify the number of data values with the gender given by the row heading and the age given by the column heading. Such a cross tabulation could be helpful in understanding the relationship between gender and age.

A number of graphical methods are available for describing data. A bar graph is a graphical device for depicting qualitative data that have been summarized in a frequency distribution. Labels for the categories of the qualitative variable are shown on the horizontal axis of the graph. A bar above each label is constructed such that the height of each bar is proportional to the number of data values in the category. A bar graph of the marital status for the 100 individuals in the above example is shown in Figure 1 . There are 4 bars in the graph, one for each class. A pie chart is another graphical device for summarizing qualitative data. The size of each slice of the pie is proportional to the number of data values in the corresponding class. A pie chart for the marital status of the 100 individuals is shown in Figure 2 .

A histogram is the most common graphical presentation of quantitative data that have been summarized in a frequency distribution. The values of the quantitative variable are shown on the horizontal axis. A rectangle is drawn above each class such that the base of the rectangle is equal to the width of the class interval and its height is proportional to the number of data values in the class.

Presentation of Statistical Data

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Data are collected often in raw form. These are then not useable unless summarized. The techniques of presentation in tabular and graphical forms are introduced. Some illustrations provided are real-world examples. Graphical presentations cover bar chart, pie chart, histogram, frequency polygon, pareto chart, frequency curve and line diagram.

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Article Sections

• Section 1: When Are Statistics Needed and What Is the Purpose of Statistics in a Research Paper?
• What goes in the Materials and Methods section?
• What goes in the Results section?
• Additional details and descriptions about design, data collection, and analysis
• Pointers for Writing about Statistics for the Horticultural Sciences

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Best Practices for Presenting Statistical Information in a Research Article

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A key characteristic of scientific research is that the entire experiment (or series of experiments), including the data analyses, is reproducible. This aspect of science is increasingly emphasized. The Materials and Methods section of a scientific paper typically contains the necessary information for the research to be replicated and expanded on by other scientists. Important components are descriptions of the study design, data collection, and statistical analysis of those data, including the software used. In the Results section, statistical analyses are presented; these are usually best absorbed from figures. Model parameter estimates (including variances) and effect sizes should also be included in this section, not just results of significance tests, because they are needed for subsequent power and meta-analyses. In this article, we give key components to include in the descriptions of study design and analysis, and discuss data interpretation and presentation with examples from the horticultural sciences.

This article provides recommendations for statistical reporting in a research journal article. Appropriate and informative reporting, and the wise use of statistical design and analysis throughout the research process, are both essential to good science; neither can happen without the other. In addition, many journals now require access to original data and the code used for analyses. This article is not a statistics tutorial; we do not explain how to do any of the statistical methods mentioned. There are many, many papers and books that provide that information; some are cited in our reference and selected reading section. Instead, we give guidelines for horticultural scientists on how best to incorporate and present statistical information in a scientific paper. We also focus on experimental rather than observational studies. To do the latter justice would require greatly expanding this article, and the majority of papers published by the American Society for Horticultural Scientists are experimental studies. A very useful complementary article is by Onofri et al. (2010) , which gives specific advice for many issues we treat only generally.

This paper is divided into two sections, as follows:

Section 1. When Are Statistics Needed and What Is the Purpose of Statistics in a Research Paper?

Section 2. Recommendations for Writing about Statistics in a Research Paper

What Goes in the Materials and Methods Section?

What Goes in the Results Section?

Additional Details and Descriptions about Design, Data Collection, and Analysis

Literature Cited and Selected References

The scope of horticultural research is large and not all studies require statistics. For example, anatomical and morphological studies can be purely descriptive. With that said, these kinds of descriptive studies are a subset of observational studies, which also include studies at the genomic, ecologic, and landscape level. For observational studies, there are useful methods for determining associations, clusters, and dimension reduction, to name a few, that are statistics based. In this article we focus primarily on research questions that require inferential statistics. Typically, using designed experiments when addressing a research question requires experiment planning, data collection, and subsequent statistical analysis, and the following recommendations are applicable.

The statistical section in an article serves five general functions. First, the design, data collection, method of analysis, and software used must be described with sufficient clarity to demonstrate that the study is capable of addressing the primary objectives of the research. When adequate information is provided, it allows for an informed peer review and for readers, in principle, to reproduce the study, including the data analysis . Second, authors must provide sufficient documentation to create confidence that the data have been analyzed appropriately. This includes verifying required statistical assumptions and justifying choices—such as the chosen mean comparison procedure and any other method that might affect results and conclusions, such as controlling for experimental-wise error. Experiment-wise error rate (or family-wise error rate, depending on how family is defined) is the probability of committing at least one Type I error throughout the whole experiment. Although the error rate for an individual hypothesis test may be small, if one tests many hypotheses, one becomes more likely to declare false significance for at least one. If the tests are not independent (e.g., using the same plants to test multiple attributes or over time, as is common in this field), this can increase the experiment-wise error rate. For example, if a plant in one treatment group is diseased, this will affect all the (correlated) measures of that group, and thus all hypotheses tests. Third, data and their analyses must be presented coherently. The statistical model and analysis should naturally follow from the study design, and be consistent with relevant characteristics of the data, such as the underlying sampling distribution (e.g., normal, Poisson, binomial). Figures and tables should illustrate, and be consistent with, important results from the analysis. Fourth, readers should not have to guess which scientific questions the analysis answers. Effects deemed statistically significant must also be shown to be biologically/economically important. Effects of potential biologic/economic importance but whose statistical significance is not supported by the data should also be reported. There is an implicit assumption of adequate power when discussing results from any statistical tests. Power is estimated during the design phase using results from previous experiments or parameter estimates from the literature. Fifth, readers should be able to use information in the statistical reporting section as a resource for planning future experiments. Variance estimates are especially important for this function.

The goal of this article is to provide an overview of how best to communicate statistics used in horticultural research. Therefore, it does not include specifics to address every contingency. Statistical methods continuously change, with new methods developed to address advances in biologic and ecologic research. For many studies, traditional and familiar methods (a.k.a. “standard statistics”) are adequate. However, for other studies, newer, less familiar methods are preferable, if not essential. Use of newer methods should not be an obstacle for publication.

Section 2: Recommendations for Writing about Statistics in a Research Paper

The following sections outline key points that should be addressed in the Materials and Methods section, and in the Results section of a journal article. Kramer et al. (2016) document common statistical problems for a sample of horticultural articles and should be used as a checklist of mistakes to avoid. The work by Reinhart (2015) is not overly technical and it explains many of these issues and other mistakes further, mostly in a biologic context.

Broadly speaking, there are two main statistical areas that the Materials and Methods section should address: 1) how was the study designed and 2) how were the data analyzed. Recommendations are grouped by subtopic.

Design and data collection.

The main idea of this section is to provide all information relevant to subsequent statistical analysis and interpretation about the design—specifically, how the experiment was conducted, how the data were collected and subsequently handled up to the point when the data were ready for statistical analysis. These are detailed next.

Describe the design. There are two components of experimental design: the experiment design and the treatment design. Both must be described.

The treatment design refers to the organization of treatment factors. Factorial designs (e.g., varieties × potting substrate) and dose–response (e.g., amount of nutrient applied) are familiar examples.

The experiment design refers to how the experimental units were organized and how randomization was done. Familiar examples are the completely randomized design (CRD) and randomized complete block design (RCBD). Any restrictions on randomization (e.g., blocking) or other ways observations were grouped must be described; this is part of the experiment design.

Describe covariates, if any. Provide the units of replication (the experimental unit; in other words, the smallest unit to which treatments were assigned independently) and the units of observation (sampling unit). The units of replication may differ for different factors (as they do, for example, in a split-plot design).

Describe how data were collected and how samples were pooled/batched, if this was done. Identify whether these were one-time measurements, multiple measurements on the plant/plot at the same time, repeated measures over time, or measurements on different plant characteristics.

Provide numbers, so it is clear how many units were in each block/group, how many received each treatment, and so on. Total sample size must be easily calculated, if not given. If a power analysis was used to determine the sample size, provide details. If not, explain how the sample size was determined. For example, one could write: “Growth chambers were limited to 30 plants, and three growth chambers were available. Previous studies using a similar setup and similar plant numbers had no difficulty detecting even moderate differences in growth patterns.”

Identify which variables are dependent (i.e., the response variables one measures, such as yield, biomass, time to flowering, elemental concentration) and which are independent (see the previous description of treatment design).

Describe any transformation of variables (e.g., logarithmic transformation) and the reason it was needed; this applies to both dependent and independent variables. Often, dependent variables can be fit without transformation if the appropriate sampling distribution is specified in a generalized linear model. When this is possible, generalized linear models are preferable to variance stabilizing transformations.

Data analysis.

Broadly speaking, data analysis includes the following steps:

Plot the original data to visualize what has happened in terms of treatment effects, distribution of data, and other features of the data deemed to be important.

Determine a statistical model consistent with the study design and the distribution of the data, and mean comparison procedures needed to address the objective of the research.

Determine the statistical assumptions associated with the selected model.

Select the software to be used to implement the analysis.

Run the analysis and verify that the assumptions are satisfied.

Report in the Materials and Methods section how the previous steps were completed.

Report the outcome of the analysis in the Results section.

There is no one-size-fits-all way of presenting the results of a statistical analysis. This is true for many aspects of using statistics in horticultural science, making it impossible to give advice covering every situation; instead, we provide general guidelines. Authors must decide what best tells the story of their research results. Tables and figures are common methods of presenting data results. The following are principles to follow:

If you include graphics showing the data, presenting data summaries, or depicting results from modeling, the intent is to portray the findings of the research accurately and make it easier for readers to visually understand the data, estimates and findings from the analysis.

Statistics that appear in both figures and tables should be consistent with the way the data were analyzed. If objectives are addressed using descriptive statistics, then these should appear in a figure or table, along with their appropriate measures of variability.

If the objectives are addressed using a statistical model, as is usually the case, then statistics obtained from the model should appear in the figure or table, along with their appropriate measures of variability.

For modeling results and hypothesis testing, there are two main categories of output from statistical software that should be presented: 1) diagnostic information demonstrating that the method and statistical model used are appropriate and 2) parameter estimates and hypothesis tests that bear directly on the research objectives. The connection to the research objectives must be clear for each statistical result (do not simply copy results produced by software). Two other categories of statistical results should be considered: 1) estimates of quantities from the model that may be useful in future research (e.g., variance estimates) and 2) statistical support for unexpected findings.

Demonstrate that model assumptions were satisfied (this could be just a sentence for simple models). See the previous point.

For multiple dependent variables, give the correlations among these variables [and possibly the correlations separately for each treatment if the treatments affect the correlations (discussed later)]. Experiment-wise error control may be necessary.

Statistics for the Materials and Methods section.

The Materials and Methods section should address the first function given in Section 1. The design, data collection, method of analysis, and software used must be described clearly. When choices were made or when nonstandard procedures were used must be justified.

Description of the study design.

This means “design” as broadly defined. If data were collected, whether from an observational study, a survey, or a designed experiment, there was a design. At a minimum, all designs include three elements: The first is the response variable (i.e., the outcome or outcomes measured), the second is the treatment design (i.e., the treatments or conditions being evaluated), and the third is the design structure of the experiment, which includes the units of replication (called the experimental unit in designed experiments), the units of observation (called the sampling unit in designed experiments), and grouping of units, if any. Grouping may consist of blocking, research conducted at multiple locations, or data collected on multiple occasions.

The following are three scenarios to illustrate these points. Scenario 1: Suppose there are plants in flats on a bench. If treatments are assigned randomly and applied to the bench, the bench is the experimental unit. If observations are made on the flat, then the flat is the unit of observation (sampling unit). This is a CRD. Scenario 2: If treatments are assigned randomly to individual flats within each bench, then flat is the experimental unit. Bench is a blocking factor. If observations are made on the flat, then the flat is the unit of observation. Notice that the experimental unit and the sampling unit can be identical. This is not the case in scenario 1. This is an RCBD. Scenario 3: Experiments with factorial treatment designs often have different-size experimental units for different factors. In this scenario, irrigation or nutrients are applied using drip lines across a bench, but each bench has several flats, with a different variety in each flat. Here, bench is the experimental unit with respect to irrigation/nutrient and flat is the experimental unit with respect to variety. In design language, this is a split-plot experiment, with the bench as the whole-plot experimental unit, irrigation/nutrient is the whole-plot treatment factor, flat is the split-plot experimental unit, and variety is the split-plot treatment factor. See Onofri et al. (2010) for another good example illustrating true and pseudo-replication.

Important note: Although it is acceptable to name the design, such as an RCBD or Latin square design, a name alone is insufficient and may be misleading. So regardless of whether a design name is used, authors must give the treatment factors, the experimental units, sampling units, and the blocking criteria (if any). For example, an RCBD may or may not have treatments replicated in each block. If treatments are replicated, one can test whether a treatment effect is the same in all blocks; if not, one has to assume it is. So, “RCBD” does not contain all the necessary information about the design.

Data collection.

This means list the response variables measured and describe how each was measured. It is also beneficial to make various plots of the original data to determine if there is a treatment effect (these plots are not necessarily included in the published paper). The biology should lead the statistics. Beyond this, you are looking for two things. When you describe the response variable, you want to focus on the sampling distribution of the response variable because this affects the model selected for the analysis of the data. You should plot the response variable against the predictor variables and look for recognizable patterns—in particular, to determine if (and how) variability changes systematically with the mean. For example, these may be scatterplots or boxplots. Another useful plot groups observations in a natural way (say, by treatment combination) and plots the means of the groups against their standard deviations. Many statistical methods assume the response variable is normally distributed, in which case variability should be roughly the same throughout the range of the response variable. A histogram of the residuals from the appropriate model with a normally distributed response variable results in a bell-shaped distribution. Note that a histogram of the raw response variable should not have a bell-shaped distribution because, if there really are treatment effects, the histogram should have a peak at each treatment mean.

Many commonly measured response variables in horticulture have a non-normal distribution. For example, germination rate (number of seeds germinated successfully/the number planted) has a binomial distribution. Many variables are continuous but have strongly right-skewed distributions, such as berry weight. A log-normal distribution often works well for this response variable. Generalized linear models allow the data to arise from many processes; the normal distribution is just one of several. Others include the log-normal, gamma, exponential, beta, binomial, Poisson, and negative binomial. The latter three are used to model count data. Again, plots used to assess the data and suggest models are part of your toolbox for determining the formal statistical analysis you will conduct, but usually are not included in an article.

The second thing you are looking for is any aspect of the data collection process that might affect the structure of the experiment design. Milliken and Johnson (2009) give examples in which the data collection process alters the study design. In one example, plants were grown in multiple distinct blocks, but then material for each treatment was combined from all blocks to allow measurement of the micronutrients of interest. The original blocks were legitimate replicates, but combining material precludes estimating block-to-block variability, effectively creating an unreplicated experiment. For this reason, a clear description of the data collection process is essential.

Model description.

Model description consists of giving the assumed distribution of the response variable and the sources of variation in the treatment and experiment design.

Scenario 1: plants assigned to benches in a CRD. The model would simply be Response = Treatment + Experimental error. (Plant-to-plant variability should be the largest contributor to the experimental error component.)

Scenario 2: treatments assigned to flats in an RCBD, with benches as the blocking criteria. The model would be Response = Treatment + Benches + Experimental error. This model assumes the treatment effect does not differ from bench to bench.

Scenario 3: Irrigation is the whole-plot treatment factor, benches are the whole-plot experimental units, variety is the split-plot treatment factor, and flat is the split-plot experimental unit. The model is Response = Irrigation treatment + Whole-plot error + Variety + Irrigation × Variety + Split-plot error. This model assumes the irrigation effect does not differ from bench to bench and that the variety effect does not differ from flat to flat. [In statistical jargon, there is no interaction between any of the fixed effects (irrigation and variety) and any of the random effects (bench and flat)].

Other aspects of analysis.

Because of the wide range of research subject matter and scales (laboratory to field), we give general principles. First, the statistical software used to analyze the data is not the method of analysis. Authors must first describe clearly the statistical procedures to compare or otherwise characterize the treatments. As illustrated in the three previous scenarios, the method of analysis must be consistent with the study design and data collection process. If there are assumptions critical to the validity of the method of analysis used, authors must state that the assumptions were met and how those assumptions were verified. If it is unclear what the assumptions are or how to verify them, talk to a statistician. Third, there must be a clear connection between the statistical methods used and the primary objectives of the research. This is where treatment design comes in, and it is important to match how you compare the treatments with the treatment design. For example, if you are comparing different varieties, then a mean comparison test is appropriate. Depending on the relative seriousness of Type I (false positives) and Type II (false negatives) errors, there are different ways to implement a means comparison test. At one extreme are two tests: Duncan multiple ranges test and an unprotected least significant difference test, neither of which control Type I error. At the other extreme are Scheffé and Bonferroni tests, which offer extreme control of Type I error at the expense of Type II error. There is a time and place for each test. Authors must state which procedure was used and why that procedure was chosen. The treatment design for experiments yielding genomic data is often simple, but the analyses are complicated. When analyzing RNAseq and similar genomic data, controlling for false discovery rate (which is also a multiple-comparisons issue) is similarly important.

In addition to factorial treatment designs [when main effects (factors with discrete levels) and their interactions are important], regression (when one or more predictor variables are continuous) is often used in horticulture. In some cases, continuous predictor variables are observational in nature. They are often called covariates in designs that also have factors. The distribution of the response variable needs to be stated because that distribution, in part, determines which statistical model is appropriate.

When the assumptions underlying a parametric method are violated, “nonparametric” methods should be used. These are not assumption-free; one assumption is that the response variable has the same sampling distribution across treatments (e.g., always skewed to the right).

Ratios constructed of two random variables (e.g., root mass/aboveground mass) have poor statistical properties (the assumptions of a parametric test are often violated because the variance of the ratios is not well determined). If ratios need to be used in an analysis, consider obtaining advice from a statistician familiar with the analysis of ratio data.

The trend in biological, medical, and social sciences journals is also to report effect sizes rather than simply the results of a significance test [see Nakagawa and Cuthill (2007) for a readable justification and concrete suggestions]. This now required in many journals ( Tressoldi et al., 2013 ).

With software improvements, Bayesian statistical methodology is gaining acceptance among biologists. In certain cases, such as models with layers of random effects, Bayesian methods enable analyses that would otherwise not be possible. In simpler models, there is often not much difference between results from Bayesian and frequentist (“traditional”) statistical analyses unless there is relevant prior information that improves the accuracy and precision of parameter estimates. Findings based on the use of Bayesian methodology are, in principle, acceptable in most biological journals, although require more explanation for readers to understand the results.

It may not be clear at the onset of an analysis which statistical methodology should be used, and several different kinds of analyses may be done with the same data set to determine which one makes the most sense. For example, diagnostics following fitting a model may suggest that the assumptions are not met. Alternative models may be examined to determine whether they fit the data better. This is not a free pass to try models until one finds the results one desires. Rather, one oscillates between fitting models and judging them using diagnostics until one is satisfied that one has selected a model that both captures the essential features of the data and has its assumptions satisfied. A useful discussion on obvious and not-so-obvious biases resulting from such a path is given by Gelman and Loken (2014) . Note that if two reasonable statistical models give contradictory conclusions, authors could present both, as long as sufficient information for the reviewers and readers to understand the issue is provided.

Statistical software.

After authors have described the method of analysis, following guidelines given previously, then any software used for statistical analyses should be cited, including online software. Include the version (the release) in the citation. Software developed by the authors for the analysis and, thus, not generally available should be explained sufficiently (perhaps in an appendix) for readers to understand what it does and why off-the-shelf software was not suitable. Authors must make the software available for others to use upon request and should include well-documented copies of the code for the reviewers. If the software was part of a system, such as SAS ® or R, authors must also give the specific procedure used, such SAS PROC GLIMMIX or the lme4 package in R.

Statistics for the Results section.

As with the method of analysis, there is no one-size-fits-all rule for presentation of data and associated formal statistical analysis. Again, we provide general principles.

First, data should be presented so that the relevant information with regard to the study’s primary objectives and most important findings are clear. Presentation may be via figures or tables, as long as these figures or tables inform rather than inadvertently hide or distort important information. In general, a picture is worth a thousand numbers. Well-conceived figures tend to portray the data’s important messages more understandably than tables.

If multiple responses are measured on the same sampling unit, such as weight, height, sugar content, and macro- and micronutrient content in a plant, correlation among these variables is likely and should be accounted for in the analysis (this is a kind of repeated-measures design) and correlation coefficients should be provided. Note that these correlations may change with different treatments or environments, just as mean responses may, so a single set of correlation coefficients may not summarize adequately the relationships among the variables in the experiment. If multiple responses are measured, experiment-wise error control may be needed. The same considerations for balancing Type I and Type II error rates could be applied here, as mentioned earlier.

Anytime means are compared, the standard error of the difference must be reported. In most cases, the standard error of a mean can be considered optional. This is admittedly a break with tradition, but it is an essential one. A plot depicting means with standard error bars is, by itself, insufficient.

Formal statistics.

Formal statistics include results of hypothesis tests (e.g., F or t statistics, P values), results of mean separation tests, estimates of means, differences, regression coefficients and their associated standard errors or confidence intervals, predicted values and their associated prediction intervals, and so on. In general, providing the mean (or mean difference) and its confidence interval is preferable to reporting only the results of a hypothesis test. Formal statistics should accompany and provide support for, but not substitute for, the depictions of the data described earlier. The American Statistical Association issued a policy statement in 2016 ( Wasserstein and Lazar, 2016 ) that clarifies legitimate vs. illegitimate uses and interpretations of P values associated with hypothesis tests. P values tell us whether the observed differences in the data are likely the result of chance or whether there is strong evidence of a true difference. They cannot tell us whether the difference is big enough to matter.

The main message should be that the observed difference is biologically, economically, or scientifically consequential, not that a P value was statistically significant. If the treatment group differs significantly from the control group, the emphasis should be on the biological consequences of finding a difference of that magnitude. If a regression line has a significant slope, the emphasis should be on the functional relationship between the independent and dependent variables. What underlying biological principle is responsible for a slope of this size? Let biology lead and let significance tests follow.

Often, not finding a statistically significant difference is important and should be reported if there was sufficient power to detect a biologically important difference. For example, if a study is done on the assumption (perhaps based on conventional wisdom or a previous research report) that a treatment difference exists, and data from a new study suggest otherwise, that information should be reported. Journals do science a major disservice by preferentially reporting only statistically significant results. This practice is called “publication bias” and is increasingly recognized to be a serious issue in all sciences. Sometimes a nondifference is the most important finding.

Many terms have technical meanings in statistics, as well as more general—and less precise—uses in common language. For example, “significant” has a specific definition in hypothesis testing, but the words “significant” and “important” tend to be used loosely and interchangeably when describing scientific results. It is best to avoid ambiguities in your writing (What is the meaning of “significant findings?”) Instead, describe the difference. For example, for a dry weight measurement, treatment A resulted in a heavier plant than treatment B. Commonly used statistical terms (e.g., analysis of variance) do not need to be defined in the article. Less common ones (e.g., reliability) do need accompanying definitions. If a reference needs to be given for a statistical technique, refer to an easily available (and commonly used) textbook if possible. The second choice would be an article in a horticulture or other biological journal. The third choice is a review article that explains the technique and perhaps compares it with others. The last choice is an article in the statistical literature that requires an advanced background in statistical theory.

Readers of an article may have a different reason for looking at results than the author’s stated purpose (e.g., to compare some of the results in the article with data readers have from a location they use, rather than the within-location comparison of cultivars in the article), which is another reason why summary information about the original data (e.g., means and standard deviations) needs to be provided. Data summaries may also be used in a subsequent meta-analysis; these typically use means, standard deviations, and other estimated parameters (e.g., block-to-block variance).

Statistics, and figures and tables.

Scientific publications are replete with tables, figures, and plots that are easy to read, technically impressive, pretty to look at, but, unfortunately, can be misleading in their content with respect to the objectives of the research they are intended to portray. If a figure shows the results of statistical modeling (e.g., means and their standard errors), you should try including the original data in the figure, perhaps in the background. This helps readers assess the adequacy of the statistical model visually. Rather than reiterate the advice of others, we suggest an excellent source for describing how data (and legends) should be presented: How to Report Statistics in Medicine ( Lang and Secic, 2006; pp. 325–393).

Plant scientists are not expected to know everything when conducting research, and this is becoming more evident with increasing collaborations across fields of study. Plant scientists should know, however, when they need input from a statistician. If so, we advise meeting with a statistician before setting up the experiment. A statistician will not be able to help after data from a poorly designed experiment are collected (other than to suggest rerunning the experiment with a better design).

A well-designed experiment can often be analyzed a number of ways and, usually, there are choices to make along the way. Examples include whether there is overdispersion, whether interaction terms are necessary, or whether a multivariate analysis should be considered to account for correlation among response variables. Should the statistician be extensively involved in the design and analysis, they should be included on the grant and/or the resulting journal article.

The following references are excellent sources for additional information about the statistical topics described in this article.

Bolker, B.M. , Brooks, M.E. , Clark, C.J. , Geange, S.W. , Poulsen, J.R. , Stevens, M.H. & White, J.S. 2009 Generalized linear mixed models: A practical guide for ecology and evolution Trends Ecol. Evol. 24 127 135

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• Export Citation

Cochran, W.G. & Cox, G.M. 1957 Experimental designs. 2nd ed. Wiley, New York, NY

Cohen, J. 1992 A power primer Psychol. Bull. 112 155 159

Gelman, A. & Loken, E. 2014 The statistical crisis in science: Data-dependent analysis—a “garden of forking paths”—explains why many statistically significant comparisons don’t hold up Amer. Sci. 102 460

James, G. , Witten, D. , Hastie, T. & Tibshirani, R. 2013 An introduction to statistical learning. Springer, New York, NY

Keselman, H.J. 2015 Per family or familywise Type I error control: “Eether, eyether, neether, nyther, let’s call the whole thing off!” J. Mod. Appl. Stat. Methods 14 1 6

Kramer, M.H. , Paparozzi, E.T. & Stroup, W.W. 2016 Statistics in a horticultural journal: Problems and solutions J. Amer. Hort. Sci. 141 400 406

Lang, T.A. & . Secic, M 2006 How to report statistics in medicine: Annotated guidelines for authors, editors and reviewers. 2nd ed. American College of Physicians. Sheridan Press, Chelesa, MI

Little, T.M. 1978 If Galileo published in HortScience HortScience 13 504 506

Milliken, G.A. & Johnson, D.E. 2009 Analysis of messy data. Vol. 1, 2nd ed. Chapman & Hall/CRC Press, Boca Raton, FL

Nakagawa, S. & Cuthill, I.C. 2007 Effect size, confidence interval and statistical significance: A practical guide for biologists Biol. Rev. Camb. Philos. Soc. 82 591 605

Onofri, A. , Carbonell, E.A. , Piepho, H.-P. , Mortimer, A.M. & Cousens, R.D. 2010 Current statistical issues in Weed Research Weed Res. 50 524

Reinhart, A. 2015 Statistics done wrong: The woefully complete guide. No Starch Press, San Francisco, CA

Schabenberger, O. & Pierce, F.J. 2002 Contemporary statistical models for the plant and soil sciences. CRC Press, Boca Raton, FL

Stroup, W.W. 2013 Generalized linear mixed models: Modern concepts, methods and applications. CRC Press, Boca Raton, FL

Stroup, W.W. 2015 Rethinking the analysis of non-normal data in plant and soil science Agron. J. 107 811 827

Tressoldi, P.E. , Giofré, D. , Sella, F. & Cumming, G. 2013 High impact = high statistical standards? Not necessarily so PLoS One 8 2 E56180 doi: 10.1371/journal.pone.0056180

Vance, E.A. 2015 Recent developments and their implications for the future of academic statistical consulting centers Amer. Stat. 69 127 137

Wasserstein, R.L. & Lazar, N.A. 2016 The ASA’s statement on p -values: Context process, and purpose Amer. Stat. 70 129 133

Weissgerber, T.L. , Milic, N.M. , Winham, S.J. & Garovic, V.D. 2015 Beyond bar and line graphs: Time for a new data presentation paradigm PLoS Biol. 13 4 E1002128 doi:10.1371/journal.pbio.1002128

Contributor Notes

We thank the reviewers for their excellent comments and reference recommendations.

1 Corresponding author. E-mail: [email protected] .

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It is the simplest form of data Presentation often used in schools or universities to provide a clearer picture to students, who are better able to capture the concepts effectively through a pictorial Presentation of simple data.

2. Column chart

It is a simplified version of the pictorial Presentation which involves the management of a larger amount of data being shared during the presentations and providing suitable clarity to the insights of the data.

3. Pie Charts

Pie charts provide a very descriptive & a 2D depiction of the data pertaining to comparisons or resemblance of data in two separate fields.

4. Bar charts

A bar chart that shows the accumulation of data with cuboid bars with different dimensions & lengths which are directly proportionate to the values they represent. The bars can be placed either vertically or horizontally depending on the data being represented.

5. Histograms

It is a perfect Presentation of the spread of numerical data. The main differentiation that separates data graphs and histograms are the gaps in the data graphs.

6. Box plots

Box plot or Box-plot is a way of representing groups of numerical data through quartiles. Data Presentation is easier with this style of graph dealing with the extraction of data to the minutes of difference.

Map Data graphs help you with data Presentation over an area to display the areas of concern. Map graphs are useful to make an exact depiction of data over a vast case scenario.

All these visual presentations share a common goal of creating meaningful insights and a platform to understand and manage the data in relation to the growth and expansion of one’s in-depth understanding of data & details to plan or execute future decisions or actions.

Importance of Data Presentation

Data Presentation could be both can be a deal maker or deal breaker based on the delivery of the content in the context of visual depiction.

Data Presentation tools are powerful communication tools that can simplify the data by making it easily understandable & readable at the same time while attracting & keeping the interest of its readers and effectively showcase large amounts of complex data in a simplified manner.

If the user can create an insightful presentation of the data in hand with the same sets of facts and figures, then the results promise to be impressive.

There have been situations where the user has had a great amount of data and vision for expansion but the presentation drowned his/her vision.

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• Many consumers or higher authorities are interested in the interpretation of data, not the raw data itself. Therefore, after the analysis of the data, users should represent the data with a visual aspect for better understanding and knowledge.
• The user should not overwhelm the audience with a number of slides of the presentation and inject an ample amount of texts as pictures that will speak for themselves.
• Data presentation often happens in a nutshell with each department showcasing their achievements towards company growth through a graph or a histogram.
• Providing a brief description would help the user to attain attention in a small amount of time while informing the audience about the context of the presentation
• The inclusion of pictures, charts, graphs and tables in the presentation help for better understanding the potential outcomes.
• An effective presentation would allow the organization to determine the difference with the fellow organization and acknowledge its flaws. Comparison of data would assist them in decision making.

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Presentation of Data

Statistics deals with the collection, presentation and analysis of the data, as well as drawing meaningful conclusions from the given data. Generally, the data can be classified into two different types, namely primary data and secondary data. If the information is collected by the investigator with a definite objective in their mind, then the data obtained is called the primary data. If the information is gathered from a source, which already had the information stored, then the data obtained is called secondary data. Once the data is collected, the presentation of data plays a major role in concluding the result. Here, we will discuss how to present the data with many solved examples.

What is Meant by Presentation of Data?

As soon as the data collection is over, the investigator needs to find a way of presenting the data in a meaningful, efficient and easily understood way to identify the main features of the data at a glance using a suitable presentation method. Generally, the data in the statistics can be presented in three different forms, such as textual method, tabular method and graphical method.

Presentation of Data Examples

Now, let us discuss how to present the data in a meaningful way with the help of examples.

Consider the marks given below, which are obtained by 10 students in Mathematics:

36, 55, 73, 95, 42, 60, 78, 25, 62, 75.

Find the range for the given data.

Given Data: 36, 55, 73, 95, 42, 60, 78, 25, 62, 75.

The data given is called the raw data.

First, arrange the data in the ascending order : 25, 36, 42, 55, 60, 62, 73, 75, 78, 95.

Therefore, the lowest mark is 25 and the highest mark is 95.

We know that the range of the data is the difference between the highest and the lowest value in the dataset.

Therefore, Range = 95-25 = 70.

Note: Presentation of data in ascending or descending order can be time-consuming if we have a larger number of observations in an experiment.

Now, let us discuss how to present the data if we have a comparatively more number of observations in an experiment.

Consider the marks obtained by 30 students in Mathematics subject (out of 100 marks)

10, 20, 36, 92, 95, 40, 50, 56, 60, 70, 92, 88, 80, 70, 72, 70, 36, 40, 36, 40, 92, 40, 50, 50, 56, 60, 70, 60, 60, 88.

In this example, the number of observations is larger compared to example 1. So, the presentation of data in ascending or descending order is a bit time-consuming. Hence, we can go for the method called ungrouped frequency distribution table or simply frequency distribution table . In this method, we can arrange the data in tabular form in terms of frequency.

For example, 3 students scored 50 marks. Hence, the frequency of 50 marks is 3. Now, let us construct the frequency distribution table for the given data.

Therefore, the presentation of data is given as below:

The following example shows the presentation of data for the larger number of observations in an experiment.

Consider the marks obtained by 100 students in a Mathematics subject (out of 100 marks)

95, 67, 28, 32, 65, 65, 69, 33, 98, 96,76, 42, 32, 38, 42, 40, 40, 69, 95, 92, 75, 83, 76, 83, 85, 62, 37, 65, 63, 42, 89, 65, 73, 81, 49, 52, 64, 76, 83, 92, 93, 68, 52, 79, 81, 83, 59, 82, 75, 82, 86, 90, 44, 62, 31, 36, 38, 42, 39, 83, 87, 56, 58, 23, 35, 76, 83, 85, 30, 68, 69, 83, 86, 43, 45, 39, 83, 75, 66, 83, 92, 75, 89, 66, 91, 27, 88, 89, 93, 42, 53, 69, 90, 55, 66, 49, 52, 83, 34, 36.

Now, we have 100 observations to present the data. In this case, we have more data when compared to example 1 and example 2. So, these data can be arranged in the tabular form called the grouped frequency table. Hence, we group the given data like 20-29, 30-39, 40-49, ….,90-99 (As our data is from 23 to 98). The grouping of data is called the “class interval” or “classes”, and the size of the class is called “class-size” or “class-width”.

In this case, the class size is 10. In each class, we have a lower-class limit and an upper-class limit. For example, if the class interval is 30-39, the lower-class limit is 30, and the upper-class limit is 39. Therefore, the least number in the class interval is called the lower-class limit and the greatest limit in the class interval is called upper-class limit.

Hence, the presentation of data in the grouped frequency table is given below:

Hence, the presentation of data in this form simplifies the data and it helps to enable the observer to understand the main feature of data at a glance.

Practice Problems

• The heights of 50 students (in cms) are given below. Present the data using the grouped frequency table by taking the class intervals as 160 -165, 165 -170, and so on.  Data: 161, 150, 154, 165, 168, 161, 154, 162, 150, 151, 162, 164, 171, 165, 158, 154, 156, 172, 160, 170, 153, 159, 161, 170, 162, 165, 166, 168, 165, 164, 154, 152, 153, 156, 158, 162, 160, 161, 173, 166, 161, 159, 162, 167, 168, 159, 158, 153, 154, 159.
• Three coins are tossed simultaneously and each time the number of heads occurring is noted and it is given below. Present the data using the frequency distribution table. Data: 0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 3, 0, 0, 1, 1, 2, 3, 2, 2, 0.

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Statistical data presentation

• Korean Journal of Anesthesiology 70(3):267

• Dongguk Unversity Ilsan Hospital, Goyang, Republic of Korea

• Inje University, Sanggye Paik Hospital

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1.1 Definitions of Statistics, Probability, and Key Terms

The science of statistics deals with the collection, analysis, interpretation, and presentation of data . We see and use data in our everyday lives.

Collaborative Exercise

In your classroom, try this exercise. Have class members write down the average time—in hours, to the nearest half-hour—they sleep per night. Your instructor will record the data. Then create a simple graph, called a dot plot, of the data. A dot plot consists of a number line and dots, or points, positioned above the number line. For example, consider the following data:

5, 5.5, 6, 6, 6, 6.5, 6.5, 6.5, 6.5, 7, 7, 8, 8, 9.

The dot plot for this data would be as follows:

Does your dot plot look the same as or different from the example? Why? If you did the same example in an English class with the same number of students, do you think the results would be the same? Why or why not?

Where do your data appear to cluster? How might you interpret the clustering?

The questions above ask you to analyze and interpret your data. With this example, you have begun your study of statistics.

In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called descriptive statistics . Two ways to summarize data are by graphing and by using numbers, for example, finding an average. After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from good data. The formal methods are called inferential statistics . Statistical inference uses probability to determine how confident we can be that our conclusions are correct.

Effective interpretation of data, or inference, is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.

Statistical Models

Statistics, like all other branches of mathematics, uses mathematical models to describe phenomena that occur in the real world. Some mathematical models are deterministic. These models can be used when one value is precisely determined from another value. Examples of deterministic models are the quadratic equations that describe the acceleration of a car from rest or the differential equations that describe the transfer of heat from a stove to a pot. These models are quite accurate and can be used to answer questions and make predictions with a high degree of precision. Space agencies, for example, use deterministic models to predict the exact amount of thrust that a rocket needs to break away from Earth’s gravity and achieve orbit.

However, life is not always precise. While scientists can predict to the minute the time that the sun will rise, they cannot say precisely where a hurricane will make landfall. Statistical models can be used to predict life’s more uncertain situations. These special forms of mathematical models or functions are based on the idea that one value affects another value. Some statistical models are mathematical functions that are more precise—one set of values can predict or determine another set of values. Or some statistical models are mathematical functions in which a set of values do not precisely determine other values. Statistical models are very useful because they can describe the probability or likelihood of an event occurring and provide alternative outcomes if the event does not occur. For example, weather forecasts are examples of statistical models. Meteorologists cannot predict tomorrow’s weather with certainty. However, they often use statistical models to tell you how likely it is to rain at any given time, and you can prepare yourself based on this probability.

Probability

Probability is a mathematical tool used to study randomness. It deals with the chance of an event occurring. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is 1 2 1 2 or .5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction 996 2,000 996 2,000 is equal to .498 which is very close to .5, the expected probability.

The theory of probability began with the study of games of chance such as poker. Predictions take the form of probabilities. To predict the likelihood of an earthquake, of rain, or whether you will get an A in this course, we use probabilities. Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent. A stockbroker uses probability to determine the rate of return on a client's investments.

In statistics, we generally want to study a population . You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a sample . The idea of sampling is to select a portion, or subset, of the larger population and study that portion—the sample—to gain information about the population. Data are the result of sampling from a population.

Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students' grade point averages. In presidential elections, opinion poll samples of 1,000–2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16-ounce can contains 16 ounces of carbonated drink.

From the sample data, we can calculate a statistic. A statistic is a number that represents a property of the sample. For example, if we consider one math class as a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. Since we do not have the data for all math classes, that statistic is our best estimate of the average for the entire population of math classes. If we happen to have data for all math classes, we can find the population parameter. A parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.

One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. In order to have an accurate sample, it must contain the characteristics of the population in order to be a representative sample . We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.

A variable , usually notated by capital letters such as X and Y , is a characteristic or measurement that can be determined for each member of a population. Variables may describe values like weight in pounds or favorite subject in school. Numerical variables take on values with equal units such as weight in pounds and time in hours. Categorical variables place the person or thing into a category. If we let X equal the number of points earned by one math student at the end of a term, then X is a numerical variable. If we let Y be a person's party affiliation, then some examples of Y include Republican, Democrat, and Independent. Y is a categorical variable. We could do some math with values of X —calculate the average number of points earned, for example—but it makes no sense to do math with values of Y —calculating an average party affiliation makes no sense.

Data are the actual values of the variable. They may be numbers or they may be words. Datum is a single value.

Two words that come up often in statistics are mean and proportion . If you were to take three exams in your math classes and obtain scores of 86, 75, and 92, you would calculate your mean score by adding the three exam scores and dividing by three. Your mean score would be 84.3 to one decimal place. If, in your math class, there are 40 students and 22 are males and 18 females, then the proportion of men students is 22 40 22 40 and the proportion of women students is 18 40 18 40 . Mean and proportion are discussed in more detail in later chapters.

The words mean and average are often used interchangeably. In this book, we use the term arithmetic mean for mean.

Example 1.1

Determine what the population, sample, parameter, statistic, variable, and data referred to in the following study.

We want to know the mean amount of extracurricular activities in which high school students participate. We randomly surveyed 100 high school students. Three of those students were in 2, 5, and 7 extracurricular activities, respectively.

The population is all high school students.

The sample is the 100 high school students interviewed.

The parameter is the mean amount of extracurricular activities in which all high school students participate.

The statistic is the mean amount of extracurricular activities in which the sample of high school students participate.

The variable could be the amount of extracurricular activities by one high school student. Let X = the amount of extracurricular activities by one high school student.

The data are the number of extracurricular activities in which the high school students participate. Examples of the data are 2, 5, 7.

Find an article online or in a newspaper or magazine that refers to a statistical study or poll. Identify what each of the key terms—population, sample, parameter, statistic, variable, and data—refers to in the study mentioned in the article. Does the article use the key terms correctly?

Example 1.2

Determine what the key terms refer to in the following study.

A study was conducted at a local high school to analyze the average cumulative GPAs of students who graduated last year. Fill in the letter of the phrase that best describes each of the items below.

1. Population ____ 2. Statistic ____ 3. Parameter ____ 4. Sample ____ 5. Variable ____ 6. Data ____

• a) all students who attended the high school last year
• b) the cumulative GPA of one student who graduated from the high school last year
• c) 3.65, 2.80, 1.50, 3.90
• d) a group of students who graduated from the high school last year, randomly selected
• e) the average cumulative GPA of students who graduated from the high school last year
• f) all students who graduated from the high school last year
• g) the average cumulative GPA of students in the study who graduated from the high school last year

1. f ; 2. g ; 3. e ; 4. d ; 5. b ; 6. c

Example 1.3

As part of a study designed to test the safety of automobiles, the National Transportation Safety Board collected and reviewed data about the effects of an automobile crash on test dummies (The Data and Story Library, n.d.). Here is the criterion they used.

Cars with dummies in the front seats were crashed into a wall at a speed of 35 miles per hour. We want to know the proportion of dummies in the driver’s seat that would have had head injuries, if they had been actual drivers. We start with a simple random sample of 75 cars.

The population is all cars containing dummies in the front seat.

The sample is the 75 cars, selected by a simple random sample.

The parameter is the proportion of driver dummies—if they had been real people—who would have suffered head injuries in the population.

The statistic is proportion of driver dummies—if they had been real people—who would have suffered head injuries in the sample.

The variable X = whether driver dummies—if they had been real people—would have suffered head injuries.

The data are either: yes, had head injury, or no, did not.

Example 1.4

An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit.

The population is all medical doctors listed in the professional directory.

The parameter is the proportion of medical doctors who have been involved in one or more malpractice suits in the population.

The sample is the 500 doctors selected at random from the professional directory.

The statistic is the proportion of medical doctors who have been involved in one or more malpractice suits in the sample.

The variable X records whether a doctor has or has not been involved in a malpractice suit.

The data are either: yes, was involved in one or more malpractice lawsuits; or no, was not.

Do the following exercise collaboratively with up to four people per group. Find a population, a sample, the parameter, the statistic, a variable, and data for the following study: You want to determine the average—mean—number of glasses of milk college students drink per day. Suppose yesterday, in your English class, you asked five students how many glasses of milk they drank the day before. The answers were 1, 0, 1, 3, and 4 glasses of milk.

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• Knowledge Base

Descriptive Statistics | Definitions, Types, Examples

Published on July 9, 2020 by Pritha Bhandari . Revised on June 21, 2023.

Descriptive statistics summarize and organize characteristics of a data set. A data set is a collection of responses or observations from a sample or entire population.

In quantitative research , after collecting data, the first step of statistical analysis is to describe characteristics of the responses, such as the average of one variable (e.g., age), or the relation between two variables (e.g., age and creativity).

The next step is inferential statistics , which help you decide whether your data confirms or refutes your hypothesis and whether it is generalizable to a larger population.

Table of contents

Types of descriptive statistics, frequency distribution, measures of central tendency, measures of variability, univariate descriptive statistics, bivariate descriptive statistics, other interesting articles, frequently asked questions about descriptive statistics.

There are 3 main types of descriptive statistics:

• The distribution concerns the frequency of each value.
• The central tendency concerns the averages of the values.
• The variability or dispersion concerns how spread out the values are.

You can apply these to assess only one variable at a time, in univariate analysis, or to compare two or more, in bivariate and multivariate analysis.

• Go to a library
• Watch a movie at a theater
• Visit a national park

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A data set is made up of a distribution of values, or scores. In tables or graphs, you can summarize the frequency of every possible value of a variable in numbers or percentages. This is called a frequency distribution .

• Simple frequency distribution table
• Grouped frequency distribution table

From this table, you can see that more women than men or people with another gender identity took part in the study. In a grouped frequency distribution, you can group numerical response values and add up the number of responses for each group. You can also convert each of these numbers to percentages.

Measures of central tendency estimate the center, or average, of a data set. The mean, median and mode are 3 ways of finding the average.

Here we will demonstrate how to calculate the mean, median, and mode using the first 6 responses of our survey.

The mean , or M , is the most commonly used method for finding the average.

To find the mean, simply add up all response values and divide the sum by the total number of responses. The total number of responses or observations is called N .

The median is the value that’s exactly in the middle of a data set.

To find the median, order each response value from the smallest to the biggest. Then , the median is the number in the middle. If there are two numbers in the middle, find their mean.

The mode is the simply the most popular or most frequent response value. A data set can have no mode, one mode, or more than one mode.

To find the mode, order your data set from lowest to highest and find the response that occurs most frequently.

Measures of variability give you a sense of how spread out the response values are. The range, standard deviation and variance each reflect different aspects of spread.

The range gives you an idea of how far apart the most extreme response scores are. To find the range , simply subtract the lowest value from the highest value.

Standard deviation

The standard deviation ( s or SD ) is the average amount of variability in your dataset. It tells you, on average, how far each score lies from the mean. The larger the standard deviation, the more variable the data set is.

There are six steps for finding the standard deviation:

• List each score and find their mean.
• Subtract the mean from each score to get the deviation from the mean.
• Square each of these deviations.
• Add up all of the squared deviations.
• Divide the sum of the squared deviations by N – 1.
• Find the square root of the number you found.

Step 5: 421.5/5 = 84.3

Step 6: √84.3 = 9.18

The variance is the average of squared deviations from the mean. Variance reflects the degree of spread in the data set. The more spread the data, the larger the variance is in relation to the mean.

To find the variance, simply square the standard deviation. The symbol for variance is s 2 .

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Univariate descriptive statistics focus on only one variable at a time. It’s important to examine data from each variable separately using multiple measures of distribution, central tendency and spread. Programs like SPSS and Excel can be used to easily calculate these.

If you were to only consider the mean as a measure of central tendency, your impression of the “middle” of the data set can be skewed by outliers, unlike the median or mode.

Likewise, while the range is sensitive to outliers , you should also consider the standard deviation and variance to get easily comparable measures of spread.

If you’ve collected data on more than one variable, you can use bivariate or multivariate descriptive statistics to explore whether there are relationships between them.

In bivariate analysis, you simultaneously study the frequency and variability of two variables to see if they vary together. You can also compare the central tendency of the two variables before performing further statistical tests .

Multivariate analysis is the same as bivariate analysis but with more than two variables.

Contingency table

In a contingency table, each cell represents the intersection of two variables. Usually, an independent variable (e.g., gender) appears along the vertical axis and a dependent one appears along the horizontal axis (e.g., activities). You read “across” the table to see how the independent and dependent variables relate to each other.

Interpreting a contingency table is easier when the raw data is converted to percentages. Percentages make each row comparable to the other by making it seem as if each group had only 100 observations or participants. When creating a percentage-based contingency table, you add the N for each independent variable on the end.

From this table, it is more clear that similar proportions of children and adults go to the library over 17 times a year. Additionally, children most commonly went to the library between 5 and 8 times, while for adults, this number was between 13 and 16.

Scatter plots

A scatter plot is a chart that shows you the relationship between two or three variables . It’s a visual representation of the strength of a relationship.

In a scatter plot, you plot one variable along the x-axis and another one along the y-axis. Each data point is represented by a point in the chart.

From your scatter plot, you see that as the number of movies seen at movie theaters increases, the number of visits to the library decreases. Based on your visual assessment of a possible linear relationship, you perform further tests of correlation and regression.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Statistical power
• Pearson correlation
• Degrees of freedom
• Statistical significance

Methodology

• Cluster sampling
• Stratified sampling
• Focus group
• Systematic review
• Ethnography
• Double-Barreled Question

Research bias

• Implicit bias
• Publication bias
• Cognitive bias
• Placebo effect
• Pygmalion effect
• Hindsight bias
• Overconfidence bias

Descriptive statistics summarize the characteristics of a data set. Inferential statistics allow you to test a hypothesis or assess whether your data is generalizable to the broader population.

The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset.

• Distribution refers to the frequencies of different responses.
• Measures of central tendency give you the average for each response.
• Measures of variability show you the spread or dispersion of your dataset.
• Univariate statistics summarize only one variable  at a time.
• Bivariate statistics compare two variables .
• Multivariate statistics compare more than two variables .

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• Diagrammatic Presentation of Data

Diagrams play an important role in statistical data presentation. Diagrams are nothing but geometrical figures like lines , bars, circles , squares , etc. Diagrammatic data presentation allows us to understand the data in an easier manner.

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Advantages of diagrammatic data presentation.

• Easy to understand – Diagrammatic data presentation makes it easier for a common man to understand the data. Diagrams are usually attractive and impressive and many newspapers and magazines use them frequently to explain certain facts or phenomena . Modern advertising campaigns also use diagrams.
• Simplified Presentation – You can represent large volumes of complex data in a simplified and intelligible form using diagrams.
• Reveals hidden facts – When you classify and tabulate data, some facts are not revealed. Diagrammatic data presentation helps in bringing out these facts and also relations .
• Quick to grasp – Usually, when the data is represented using diagrams, people can grasp it quickly.
• Easy to compare – Diagrams make it easier to compare data.
• Universally accepted – Almost all fields of study like Business , economics , social institutions, administration , etc. use diagrams. Therefore, they have universal acceptability.

Browse more Topics under Descriptive Statistics

• Definition and Characteristics of Statistics
• Stages of Statistical Enquiry
• Importance and Functions of Statistics
• Nature of Statistics – Science or Art?
• Application of Statistics
• Law of Statistics and Distrust of Statistics
• Meaning and Types of Data
• Methods of Collecting Data
• Sample Investigation
• Classification of Data
• Tabulation of Data
• Frequency Distribution of Data
• Graphic Presentation of Data
• Measures of Central Tendency
• Mean Median Mode
• Measures of Dispersion
• Standard Deviation
• Variance Analysis

Limitations of Diagrammatic Data Presentation

You need to exercise caution while drawing inferences from diagrams. Here are some of their limitations:

• Provides vague ideas – While diagrams offer a vague idea about the problem, it is useful only to a common man. An expert, who seeks an exact idea of the problem cannot benefit from them.
• Limited information – Classified and tabulated data provides more information than diagrams.
• Low precision – Diagram offer a low level of precision of values.
• Restricts further data analysis – Diagrams do not allow the user to analyze the data further.
• Portrays limited characteristics – Diagrams tend to portray only a limited number of characteristics. Therefore, it is difficult to understand a large number of characteristics using diagrams.
• A possibility of misuse – Sometimes diagrams are misused to present an illusory picture of the problem.
• Fail to present a meaningful look in certain situations – If the data has various measurements and wide variation, then diagrams do not present a meaningful look.
• Careful usage – If diagrams are drawn on a false baseline, then the user must analyze them carefully.

General Principles of Diagrammatic Presentation of Data

A diagrammatic presentation is a simple and effective method of presenting the information that any statistical data contains. Here are some general principles of diagrammatic presentation which can help you make them a more effective tool of understanding the data:

• Write a suitable title on top which conveys the subject matter in a brief and unambiguous manner. If you want to provide more details about the title, then you can mention them in the footnote below the diagram.
• You must construct a diagram in a manner that immediately impacts the viewer. Ensure that you draw it neatly with an appropriate balance between its length and breadth. Further, make sure that the diagram is neither too large nor too small. You can also use different colors or shades to emphasize different aspects of the problem.
• Draw the diagram accurately using proper scales of measurement. You should never compromise accuracy for attractiveness.
• Select the design of the diagram carefully keeping in view the nature of the data and also the objective of the investigation.
• If you use different shades or colors to depict the different characteristics in the diagram, then ensure that you provide an index explaining them.
• If you are using a secondary source, then ensure that you specify the source of data.
• Try to keep your diagram as simple as possible.

Types of Diagrams

There are many types of diagrams which are used for data presentation. Some popular types of diagrams are explained below:

Line Diagram

In a line diagram, you can represent different values using lines of varying lengths. Further, these lines are either horizontal or vertical. Also, there is a uniform gap between successful lines. You can use this when the number of items is very large. Here is an example:

The income of 10 workers in a particular week was recorded as given below. Represent the data by a line diagram.

The diagram is as follows:

Simple Bar Diagram

In order to draw a simple bar diagram, you construct horizontal or vertical lines who have heights proportional to the value of the item. You choose an arbitrary width of the bar but keep it constant. Also, ensure that the gaps between the bars are constant. This diagram is suitable to represent individual time-series or a spatial series. Here is an example:

Represent the following data using a bar diagram:

Multiple Bar Diagram

You can use a multiple bar diagram or a compound bar diagram when you want to show a comparison between two or more sets of data. You can draw a set of bars side-by-side, without gaps and separate the sets of bars with a constant gap. Further, you must color or shade different bars in a different manner. Here is an example:

Represent the following data on the faculty-wise distribution of students using a multiple bar diagram:

Component or Sub-Divided Bar Diagram

In this diagram, you divide the bar corresponding to each phenomenon into various components. Therefore, the portion that each component occupies denotes its share in the total. You must ensure that the sub-divisions follow the same order and also that you use different colors or shades to distinguish them. You can use this diagram to represent the comparative values of different components of a phenomenon. Here is an example:

The following table gives the value of (A in Crores) of contracts secured from abroad, in respect of Civil Construction, industrial turnkey projects and software consultancy in three financial years. Construct a component bar diagram to denote the share of activity in total export earnings from the three projects.

Circular or Pie Chart

A pie chart consists of a circle in which the radii divide the area into sectors. Further, these sectors are proportional to the values of the component items under investigation. Also, the whole circle represents the entire data under investigation.

Steps to draw a Pie Chart

• Express the different components of the given data in percentages of the whole
• Multiply each percentage component with 3.6 (since the total angle of a circle at the center is 360°)
• Draw a circle
• Divide the circle into different sectors with the central angles of each component
• Shade each sector differently

Use of Pie Chart

The use of pie charts is quite popular as the circle provides a visual concept of the whole. Pie charts are simple to use and hence are one of the most commonly used charts. However, the pie charts are sparingly used only for the following reasons:

• They are the best chart for displaying statistical information when the number of components is not more than 6. In the case of more components, the chart becomes too complex to understand.
• Pie charts are not useful when the values of the components are similar. This is because in the case of similarly sized sectors the viewer can find it difficult to differentiate between the slice sizes.

Here is an example:

Represent the following data, on India’s exports (Rs. in Crores) by regions from April to February 1997.

From the table we have,

Total exports = 32699 + 42516 + 23495 + 5133 = Rs. 103, 843 crores

Europe = \( \frac{32699 × 360}{103843} \) = 113°

Asia = \( \frac{42516 × 360}{103843} \) = 147°

America = \( \frac{23495 × 360}{103843} \) = 82°

Africa = \( \frac{5133 × 360}{103843} \) = 18°

Solved Question

Q1. What are the advantages of diagrammatic data presentation?

Answer: The advantages of diagrammatic data presentation are:

• Diagrams are easy to understand
• You can represent huge volumes of data in a simplified manner
• They reveal hidden facts
• They quick to grasp and easy to compare
• Diagrams have a universal acceptability

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Descriptive Statistics

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Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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10 Methods of Data Presentation That Really Work in 2024

Leah Nguyen • 15 July, 2024 • 13 min read

Have you ever presented a data report to your boss/coworkers/teachers thinking it was super dope like you’re some cyber hacker living in the Matrix, but all they saw was a pile of static numbers that seemed pointless and didn't make sense to them?

Understanding digits is rigid . Making people from non-analytical backgrounds understand those digits is even more challenging.

How can you clear up those confusing numbers and make your presentation as clear as the day? Let's check out these best ways to present data. 💎

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Data Presentation - What Is It?

The term ’data presentation’ relates to the way you present data in a way that makes even the most clueless person in the room understand. 

Some say it’s witchcraft (you’re manipulating the numbers in some ways), but we’ll just say it’s the power of turning dry, hard numbers or digits into a visual showcase that is easy for people to digest.

Presenting data correctly can help your audience understand complicated processes, identify trends, and instantly pinpoint whatever is going on without exhausting their brains.

Good data presentation helps…

• Make informed decisions and arrive at positive outcomes . If you see the sales of your product steadily increase throughout the years, it’s best to keep milking it or start turning it into a bunch of spin-offs (shoutout to Star Wars👀).
• Reduce the time spent processing data . Humans can digest information graphically 60,000 times faster than in the form of text. Grant them the power of skimming through a decade of data in minutes with some extra spicy graphs and charts.
• Communicate the results clearly . Data does not lie. They’re based on factual evidence and therefore if anyone keeps whining that you might be wrong, slap them with some hard data to keep their mouths shut.
• Add to or expand the current research . You can see what areas need improvement, as well as what details often go unnoticed while surfing through those little lines, dots or icons that appear on the data board.

Methods of Data Presentation and Examples

Imagine you have a delicious pepperoni, extra-cheese pizza. You can decide to cut it into the classic 8 triangle slices, the party style 12 square slices, or get creative and abstract on those slices. 

There are various ways to cut a pizza and you get the same variety with how you present your data. In this section, we will bring you the 10 ways to slice a pizza - we mean to present your data - that will make your company’s most important asset as clear as day. Let's dive into 10 ways to present data efficiently.

#1 - Tabular 

Among various types of data presentation, tabular is the most fundamental method, with data presented in rows and columns. Excel or Google Sheets would qualify for the job. Nothing fancy.

This is an example of a tabular presentation of data on Google Sheets. Each row and column has an attribute (year, region, revenue, etc.), and you can do a custom format to see the change in revenue throughout the year.

When presenting data as text, all you do is write your findings down in paragraphs and bullet points, and that’s it. A piece of cake to you, a tough nut to crack for whoever has to go through all of the reading to get to the point.

• 65% of email users worldwide access their email via a mobile device.
• Emails that are optimised for mobile generate 15% higher click-through rates.
• 56% of brands using emojis in their email subject lines had a higher open rate.

(Source: CustomerThermometer )

All the above quotes present statistical information in textual form. Since not many people like going through a wall of texts, you’ll have to figure out another route when deciding to use this method, such as breaking the data down into short, clear statements, or even as catchy puns if you’ve got the time to think of them.

#3 - Pie chart

A pie chart (or a ‘donut chart’ if you stick a hole in the middle of it) is a circle divided into slices that show the relative sizes of data within a whole. If you’re using it to show percentages, make sure all the slices add up to 100%.

The pie chart is a familiar face at every party and is usually recognised by most people. However, one setback of using this method is our eyes sometimes can’t identify the differences in slices of a circle, and it’s nearly impossible to compare similar slices from two different pie charts, making them the villains in the eyes of data analysts.

#4 - Bar chart

The bar chart is a chart that presents a bunch of items from the same category, usually in the form of rectangular bars that are placed at an equal distance from each other. Their heights or lengths depict the values they represent.

They can be as simple as this:

Or more complex and detailed like this example of data presentation. Contributing to an effective statistic presentation, this one is a grouped bar chart that not only allows you to compare categories but also the groups within them as well.

#5 - Histogram

Similar in appearance to the bar chart but the rectangular bars in histograms don’t often have the gap like their counterparts.

Instead of measuring categories like weather preferences or favourite films as a bar chart does, a histogram only measures things that can be put into numbers.

Teachers can use presentation graphs like a histogram to see which score group most of the students fall into, like in this example above.

#6 - Line graph

Recordings to ways of displaying data, we shouldn't overlook the effectiveness of line graphs. Line graphs are represented by a group of data points joined together by a straight line. There can be one or more lines to compare how several related things change over time. 

On a line chart’s horizontal axis, you usually have text labels, dates or years, while the vertical axis usually represents the quantity (e.g.: budget, temperature or percentage).

#7 - Pictogram graph

A pictogram graph uses pictures or icons relating to the main topic to visualise a small dataset. The fun combination of colours and illustrations makes it a frequent use at schools.

Pictograms are a breath of fresh air if you want to stay away from the monotonous line chart or bar chart for a while. However, they can present a very limited amount of data and sometimes they are only there for displays and do not represent real statistics.

#8 - Radar chart

If presenting five or more variables in the form of a bar chart is too stuffy then you should try using a radar chart, which is one of the most creative ways to present data.

Radar charts show data in terms of how they compare to each other starting from the same point. Some also call them ‘spider charts’ because each aspect combined looks like a spider web.

Radar charts can be a great use for parents who’d like to compare their child’s grades with their peers to lower their self-esteem. You can see that each angular represents a subject with a score value ranging from 0 to 100. Each student’s score across 5 subjects is highlighted in a different colour.

If you think that this method of data presentation somehow feels familiar, then you’ve probably encountered one while playing Pokémon .

#9 - Heat map

A heat map represents data density in colours. The bigger the number, the more colour intensity that data will be represented.

Most US citizens would be familiar with this data presentation method in geography. For elections, many news outlets assign a specific colour code to a state, with blue representing one candidate and red representing the other. The shade of either blue or red in each state shows the strength of the overall vote in that state.

Another great thing you can use a heat map for is to map what visitors to your site click on. The more a particular section is clicked the ‘hotter’ the colour will turn, from blue to bright yellow to red.

#10 - Scatter plot

If you present your data in dots instead of chunky bars, you’ll have a scatter plot. 

A scatter plot is a grid with several inputs showing the relationship between two variables. It’s good at collecting seemingly random data and revealing some telling trends.

For example, in this graph, each dot shows the average daily temperature versus the number of beach visitors across several days. You can see that the dots get higher as the temperature increases, so it’s likely that hotter weather leads to more visitors.

5 Data Presentation Mistakes to Avoid

#1 - assume your audience understands what the numbers represent.

You may know all the behind-the-scenes of your data since you’ve worked with them for weeks, but your audience doesn’t.

Showing without telling only invites more and more questions from your audience, as they have to constantly make sense of your data, wasting the time of both sides as a result.

While showing your data presentations, you should tell them what the data are about before hitting them with waves of numbers first. You can use interactive activities such as polls , word clouds , online quizzes and Q&A sections , combined with icebreaker games , to assess their understanding of the data and address any confusion beforehand.

#2 - Use the wrong type of chart

Charts such as pie charts must have a total of 100% so if your numbers accumulate to 193% like this example below, you’re definitely doing it wrong.

Before making a chart, ask yourself: what do I want to accomplish with my data? Do you want to see the relationship between the data sets, show the up and down trends of your data, or see how segments of one thing make up a whole?

Remember, clarity always comes first. Some data visualisations may look cool, but if they don’t fit your data, steer clear of them. 

#3 - Make it 3D

3D is a fascinating graphical presentation example. The third dimension is cool, but full of risks.

Can you see what’s behind those red bars? Because we can’t either. You may think that 3D charts add more depth to the design, but they can create false perceptions as our eyes see 3D objects closer and bigger than they appear, not to mention they cannot be seen from multiple angles.

#4 - Use different types of charts to compare contents in the same category

This is like comparing a fish to a monkey. Your audience won’t be able to identify the differences and make an appropriate correlation between the two data sets. 

Next time, stick to one type of data presentation only. Avoid the temptation of trying various data visualisation methods in one go and make your data as accessible as possible.

#5 - Bombard the audience with too much information

The goal of data presentation is to make complex topics much easier to understand, and if you’re bringing too much information to the table, you’re missing the point.

The more information you give, the more time it will take for your audience to process it all. If you want to make your data understandable and give your audience a chance to remember it, keep the information within it to an absolute minimum. You should end your session with open-ended questions to see what your participants really think.

What are the Best Methods of Data Presentation?

Finally, which is the best way to present data?

The answer is…

There is none! Each type of presentation has its own strengths and weaknesses and the one you choose greatly depends on what you’re trying to do. 

For example:

• Go for a scatter plot if you’re exploring the relationship between different data values, like seeing whether the sales of ice cream go up because of the temperature or because people are just getting more hungry and greedy each day?
• Go for a line graph if you want to mark a trend over time. 
• Go for a heat map if you like some fancy visualisation of the changes in a geographical location, or to see your visitors' behaviour on your website.
• Go for a pie chart (especially in 3D) if you want to be shunned by others because it was never a good idea👇

Frequently Asked Questions

What is a chart presentation.

A chart presentation is a way of presenting data or information using visual aids such as charts, graphs, and diagrams. The purpose of a chart presentation is to make complex information more accessible and understandable for the audience.

When can I use charts for the presentation?

Charts can be used to compare data, show trends over time, highlight patterns, and simplify complex information.

Why should you use charts for presentation?

You should use charts to ensure your contents and visuals look clean, as they are the visual representative, provide clarity, simplicity, comparison, contrast and super time-saving!

What are the 4 graphical methods of presenting data?

Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Leah Nguyen

Words that convert, stories that stick. I turn complex ideas into engaging narratives - helping audiences learn, remember, and take action.

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Basic Introduction to Statistics in Medicine, Part 1: Describing Data

Wyatt p. bensken.

1 Department of Population and Quantitative Health Sciences, Case Western Reserve University School of Medicine, Cleveland, Ohio, USA.

Fredric M. Pieracci

2 Department of Surgery, Denver Health Medical Center, Denver, Colorado, USA.

Vanessa P. Ho

3 Department of Surgery, MetroHealth Medical Center, Cleveland, Ohio, USA.

Background: Standardized and concise data presentation forms the base for subsequent analysis and interpretation. This article reviews types of data, data properties and distributions, and both numerical and graphical methods of data presentation.

Methods: For the purposes of illustration, the National Inpatient Sample was queried to categorize patients as having either emergency general surgery or non-emergency general surgery admissions.

Results: Variables are categorized as either categorical or numerical. Within the former, there are ordinal and or nominal subtypes; within the latter, there are ratio and interval subtypes. Categorical data are typically displayed as number (%). Numerical data must be assessed for normality as normally distributed data behave in certain patterns that allow for specific statistical tests to be used. Several properties exist for numerical data, including measurements of central tendency (mean, median, and mode), as well as standard deviation, range, and interquartile range. The best initial assessment of the distribution of numerical data is graphical with both histograms and box plots.

Conclusion: Knowledge of the types, distribution, and properties of data is essential to move forward with hypothesis testing.

Counting and measurement is the basis of all research and accurate representation of numeric data ensures that research is systematic and reproducible. After the design of a research study, the most critical juncture in a project is a complete and accurate description of the data and the methods used to obtain the results. Utilizing a systematic description of the data as a first step not only ensures transparent reporting of results, but helps the investigator identify potential problems in their analytic process or data sources to guide analytic decisions. Examining the distribution and structure of data ensures that the test and analyses chosen are the most appropriate and statistically valid. In addition to aiding the investigator, a clear description of the methods and data will aid in peer review and the study's utility in the broader research enterprise. Specifically, the description helps readers to understand external validity of a particular study, in other words, are findings generalizable to other populations? When drafting a manuscript, the description of data presentation and analysis should be standardized to the point where, after reading it, an independent party could reproduce your results exactly.

There are two cornerstones to an appropriate description of data: (1) a well-developed and presented table that describes your population, often referred to as a demographics table or Table 1 and (2) data visualization with appropriately chosen graphics. In this article, we provide examples of how to describe and visualize data using a nationally representative database, the Nationwide Inpatient Sample, to demonstrate a robust and thorough description of the methods and data used, while also highlighting specific pitfalls. We also demonstrate how weighted databases may add an extra layer of complexity to describing your study population. It is our goal that this work provides a road map for investigators seeking to utilize best practices in describing and presenting their data.

Types of Quantitative Data

To demonstrate these data science statistical practices and pitfalls, we used data from the 2017 Nationwide Inpatient Sample (NIS) from the Healthcare Cost and Utilization Project (HCUP). The NIS is an approximately 20% sample of all-payer hospitalizations that are included as part of HCUP that are then weighted to provide national estimates. This weighting means that each observed hospitalization in the sample represents a specific number of hospitalizations in the population. With this, the sample of 7.1 million hospitalizations represents more than 35.7 million hospitalizations. It includes parameters covering patient demographics (race, gender, age, payer, etc.), admission and discharge status, diagnoses, procedures, length of stay (LOS), and cost. All data are at the discharge-level and the NIS does not provide patient identifiers to be able to link hospitalizations. In this study we identified patients who underwent emergency general surgery (EGS) in 2017. Here, EGS is defined as appendectomy, colectomy and colostomy, laparotomy, laparoscopy, lysis of adhesions, small bowel resection, ulcer repair, and gallbladder procedures, as previously described by Smith et al. [ 1 ]. Specifically, we required that the hospitalization contain both a diagnosis and procedure code for EGS.

Of note, NIS data are structured to be able to perform a weighted adjustment to establish a nationally representative sample. For this article, however, the only weighted analysis we present is for the overall number of EGS procedures. This weighting followed guidelines from the Agency for Healthcare Research and Quality (AHRQ) using the given weights, cluster, and strata. Because of this weighting, the national estimates are presented with standard errors. Data cleaning was done via SAS, version 9 (SAS Institute, Cary, NC) with visualizations made in R version 3.6.1 using the tidyverse and patchwork packages [ 2 , 3 ]. Sample data available online were also used to build the skewed distributions in Figure 1 [ 4 ].

Example of normal and skewed distributions, using simulated data.

Using these data, we demonstrate how to construct a demographics table or Table 1 while also showing the value of graphical visualization of data to illustrate the distribution of age and LOS. The 2017 NIS contained 7,159,694 admissions that, when weighted, represent a national estimate of 35,798,453 hospitalizations. There was a total of 11,034 (1.6%) hospitalizations for emergency general surgery (EGS), representing an estimated 555,170 ± 5,969 (1.6% ± 0.01) nationally in 2017.

Data Cleaning and Categorization for Analysis

Data collection is typically organized via a data table, spreadsheet, or data frame. These datasets are typically organized such that each row of data represents one observation or unit to be studied (such as a single patient, one admission, or a hospital) and each column of data is a collected parameter (such as age or sex). Broadly, there are two types of variables: categorical (nominal and ordinal) and numeric (interval and ratio) ( Table 1 ). Categorical data represent named groups of observations and are not quantitative. Categorical data can be ordered (ordinal) or not ordered (nominal). In our example below, represented by Table 2 , gender, race, payer, and disposition are examples of categorical nominal variables. In the below example, the age categories (<18 years, 18–34, 35–49, etc.) are examples of ordered categorical variables.

Table of Demographics

Description of the study population, comparing those hospitalization not for EGS and those for EGS. These data come from the 2017 Nationwide Inpatient Sample. Note that two cells are presented as “<” (less than); this is due to data restrictions of displaying cells less than 11.

EGS = emergency general surgery; SD = standard deviation; IQR = interquartile range; LOS = length of stay; SNF = skilled nursing facility; ICF = intermediate care facility.

Numerical data are collected as numbers. Length of stay is an example of numerical data. Length of stay is a continuous variable, meaning that it is a measure of length, represented by the unit “days” and usually rounded to the nearest integer. Length of stay is also an example of “ratio” data, whereby the numbers are meaningfully related and zero is an absolute number. In other words, a person who had a LOS of 6 days was in the hospital twice as long as a person in the hospital for 3 days, and no one has a negative LOS. This differs from interval data. Interval data are characterized by numbers that have equal distances between values but there is no fixed beginning. An example of this is time in a 12-hour clock. These distinctions are important because some numbers should not be added or subtracted, and only ratio data can be interpreted as multiples of each other. Some numeric data should not be treated as continuous, such as injury severity scale (ISS) because an ISS of 20 is not twice as bad as an ISS of 10. Furthermore, other seemingly numeric data do not even represent numbers, such as medical record number or zip code, which should be considered categorical data because the numbers are really only assigned labels.

Numerical data can be converted to categories if the researchers believe this conversion is appropriate. However, it is important to remember that converting data from continuous to categorical necessarily results in loss of information granularity. This may limit future analyses. Age is a continuous numerical variable that consists of ratio data. In Table 2 , age is described multiple ways. As continuous numerical data, age can be represented as a distribution with a mean and standard deviation, or a median and interquartile range. Alternatively, age was also converted into a categorical ordinal variable. We elected to present standard groups, namely, <18, 18–34, 35–49, 40–64, 65–79, 80+. These groups are not even intervals but are socially representative of groups that have similar attributes (child, young adult, etc.); another way to categorize age might be by deciles. Yet another way to group numerical data would be into those either above or below the median value for that parameter. Finally, numerical data may be grouped into categories to replicate findings from previous research, in which certain groupings were found to be meaningful. The researchers can decide which data presentation is most appropriate for their study and study question, and whether “cutting” numeric data into categories is useful or advantageous to demonstrate specific concepts being studied.

Data distribution and properties

When visualizing data, we are often seeking some conclusion regarding the distribution of the data, that is the shape of the data. Frequently, researchers try to determine if data follow a normal (or bell-shaped) distribution but often encounter data that is either left-skewed or right-skewed. Figure 1 demonstrates a normal distribution as well as distributions that are both left-skewed and right-skewed. The normal distribution is often desired because it allows for a number of powerful statistical tests to be conducted with the data, such as a Student t-test and linear regression, whereas skewed distributions violate important statistical assumptions of these tests. Another common distribution found in medical research is a bimodal distribution that as two peaks, which may occur, for example, if we saw the highest frequencies of a disease or condition in young adulthood and then again in older adulthood. Whereas the normal distribution is the most commonly discussed, it is actually found in only the minority of cases. It is important to note that there are numerous other statistical distributions with their own assumptions and analyses that are beyond the scope of this article but that researchers may encounter in the literature.

Mean, median, and mode are called measures of central tendency and are the simplest way to describe where the middle of numerical data distribution lies. The arithmetic mean is the average of all the numbers (the sum of numbers divided by the total count of items that were included in the sum). Technically, numeric scales such as Likert scales or injury severity scores that are not ratio data should not be presented as means. In a 10-point Likert scale, a value of eight is not twice as large as a level of four, nor is it four times as bad as a value of two, and thus a mean value cannot really be interpreted. A mean is most appropriate when a ratio continuous variable is normally distributed, or the values are shaped like a classic bell curve. Means can also be used more confidently when sample sizes are large and are therefore more likely to follow a normal distribution.

The median value is the middle number if all numerical values are lined up sequentially. A median and range is less affected to outliers than a mean and standard deviation, which makes the median a better choice for variables with a skewed distribution, a large number of outliers, or small sample size. Because no arithmetic is used to calculate them, median values are more interpretable for things such as scales or scores that cannot be added or subtracted. The mode is the value observed frequently. For a parameter that is distributed normally, the mean, median, and mode are all the same.

In addition to measurements of central tendency, the range, interquartile range, and standard deviation are useful properties. The range is displayed as the minimum and maximum value for the variable. Reviewing the minimum and maximum values can often help identify data entry errors, for example, an age of 510 years entered by mistake when the actual age was 51 years. The interquartile range represents the 25th percentile to the 75th percentile for the variable and is typically listed after the median. Mean values are typically displayed with a standard deviation, which indicates how wide the spread of numbers is around the average value.

Demographics table example

In the example demographics table ( Table 2 ), categorical variables such as gender, race, payer, admission type, and disposition are presented as n (%) and these are relatively straightforward. Important groupings here are dependent on the researcher's aims. For example, race groups or disposition can be combined or separated.

We present multiple ways to show numerical data. Looking first at age, there is a small difference between mean and median, where the mean age for EGS and non-EGS groups is slightly lower than the median age, suggesting that there are young outliers that skew the mean age with a leftward tail. Grouping by age categories may provide extra detail about age distribution, showing more than one-half of all EGS and non-EGS admissions occur in adults over the age of 40, whereas hospitalizations for EGS occurs in a lower proportion of pediatric patients.

Alternatively, the mean values for LOS as well as total charges are much larger than the median values, suggesting that there are outliers with long LOS that skew the data to have a long rightward tail. This is common for hospital and intensive care unit LOS data. For total charges, the standard deviations are larger than the value of the means, suggesting that there is a wide variation in charges and utilizing the mean for this variable is likely not the best approach for further analysis. Thus, without even seeing the actual data, the reader can make inferences about their shape based on the differences between mean and median calculations and also on the relative size of the standard deviation compared with the mean. Familiarity with the most common shapes of data such as age and LOS will also draw attention to unusual patterns and alert readers when the incorrect statistical test is being applied.

Data description and visualization using histograms

Although there are several statistical tests to assess for normality of a certain parameter, often the most obvious method is visual interpretation of a histogram. A histogram is a visual representation of the distribution of the data, where the frequency of a value is plotted on the y-axis, typically as bars, against the value of the variable on the x-axis. We present several histograms below, overlaying the normal distribution to highlight skewness. Of note, the y-axis here is not the frequency (the number of individuals in each bin) but rather the density. The density is a re-scaling of the frequency to accommodate a true normal distribution, where the area under the curve and the sum of the area of the bars equals one. The visual shape of the distribution will be identical with either frequency or density on the y-axis. Formal comparisons of these data are presented in a follow-up article [ 5 ]. Figure 2 highlights the distribution of age between non-EGS cases and EGS hospitalizations. As suggested by the demographics table, there is a large number of young non-EGS admissions, which leads to skewing of the age data; the histogram shows this more clearly than simply the presentation of the means and medians. Note also that the non-EGS age has a tri - modal distribution, with three peaks of frequency compared with only a single peak in the EGS group.

Distribution of age (in years) stratified by those hospitalizations that were not for emergency general surgery (EGS) and those that were for EGS.

Another commonly used figure is the boxplot, seen in the lower half of Figure 3 . This is another way to demonstrate the distribution of the data and is a very efficient method of communicating data. The middle bar represents the median, the edges of the box are the first and third quartiles, and the lines (commonly called whiskers) represent the data extending to 1.5 times the interquartile range. Points outside this are displayed and represent the most extreme outliers. They are another useful visualization, especially when presenting the distribution of a value across groups (e.g., LOS stratified by race). Figures 2 and ​ and3 3 demonstrate the distribution, and particularly the skewness, of two of the continuous variables of interest: age ( Fig. 3 ) and LOS. In particular, LOS shows a skewed distribution and inflation of the mean but arriving at these conclusions can be much easier using well-developed data visualizations such as Figure 3 . In these figures we can clearly see the outliers in the boxplots, whereas the histograms confirm that the distributions do not follow a normal distribution (the black curve overlaid). Additionally, we would likely want to present the median and interquartile range when describing these variables because we know the mean and standard deviation are highly sensitive to these outliers. Although we present these figures in this article, in a study we would likely include them as a supplement for reviewers and fellow researchers to reference if needed.

Distribution, both histogram and boxplot, of the age (in years) of those hospitalizations for emergency general surgery (EGS). The y-axis of the histogram represents the density (not frequency), and the normal curve for these data is overlaid to highlight the skew in age data for this population.

Example of data description for a methods section of an article

Ideally, the methods section of an article will be comprehensive enough that would allow for your work to be reproduced. In addition to the overview, data source(s), study population, inclusion/exclusion criteria, and variables of interest (as we do in our own methods section), it is important to describe how data will be displayed. The portion of the methods that includes this information, from a hypothetical study, could be as follows: “Numerical data are expressed as median (interquartile range) and were assessed for normality using both the XXX test and visually using both histograms and boxplots. Categorical data are expressed as number (%). Because age was not distributed normally, and rather followed a bimodal distribution, this variable was converted to categorical and dichotomized around the median. Time to surgery was also not distributed normally and so converted into three categories: <24 hours, 24–72 hours, and >72 hours, based on our prior study (appropriate citation).”

The complete description of our data, as the first step of the analysis stage, is crucial to understanding the study population as well as informing our later statistical decisions. This process of describing the data can also serve as a mechanism for study validity and ensure that earlier parts of the study (e.g., data cleaning, processing, and management) did not introduce any errors. One example of this may be if we were studying a condition primarily prevalent in older adults but identified younger adults in the exploratory analysis. This would either suggest a data or coding error, which should be investigated thoroughly, or unique cases of the condition of study that may warrant exclusion.

This ability to spot errors also links to the ability to make additional study cohort restrictions to better refine the study population or remove heterogeneity. In our example of EGS, there are two key areas in our data exploration that could influence future analytic decisions: age and admission type. Of our EGS population, 8% of hospitalizations were children and 31% were 65 years old or older ( Table 1 ). In our study we would first, perhaps, exclude children from the analysis by considering potential heterogeneity or differences, in disease presentation and management across later age groups. If our study question was to examine only the geriatric population, we might restrict our analysis to the 31% that are 65 years old or older. Furthermore, although termed emergency general surgery, we identified that 16.2% of hospitalizations for EGS were labelled elective ( Table 1 ), which highlights a limitation of administrative data and use of diagnosis codes. For that reason, and in hopes of creating the most accurate case definition, we could consider restricting on both age and admission type, to focus on older adults who were non-elective admissions.

Once the study cohort has been identified and the initial descriptive statistics have been conducted, data visualization is an important next step. This visualization of the data, much like the description of the data, serves two important purposes: first it provides a way to convey important information about your study population and second it aids decisions for subsequent statistical analyses. In addition to these important principles to convey your data and findings, these visualizations can help assess the normality of variables that identifies skewness and informs the validity of statistical comparisons and regression models, discussed in more detail elsewhere. Lack of normality and distributions, would require us to utilize non-parametric analyses, which again are detailed in a follow-up article [ 5 ].

Another important consideration in the creation of a Demographics Table is whether or not to include p values. Historically, these tables have included p values as a way to identify statistically significant differences between the two groups efficiently, with a threshold of significance to be 0.05 (that is, only p values <0.05 are considered statistically significant). This statistical value was introduced to prominence by statistician Ronald Fisher in 1925 as a mechanism to assess the probability that the result obtained is as or more extreme than what was observed due to chance alone [ 6 , 7 ]. In recent years, however, there has been a shift away from the reliance on p values because of a myriad of factors, including the increasing emphasis on the threshold to determine significance or results, and the often misleading interpretation or reasoning surrounding these cut points [ 6–8 ]. One additional limitation of an arbitrary p value is that in large datasets such as the NIS, statistical significance is easily achieved even when differences between groups are small and likely not clinically or meaningfully significant. For these reasons, we have chosen not to display them and, instead, focus our description of the data on meaningful differences while leaving hypothesis testing to specific questions in comparing the data.

The final important point to raise in this article is our analysis of the unweighted data. The NIS, and many other federal and nationally representative datasets, includes weighting information, which makes it possible to create national estimates. We did present the national estimate for the number of hospitalizations, but the rest of our description was on the unweighted and thus cannot be taken as national estimates. One must think critically about the intention of the study and its goals when deciding on weighting, as weighting adds another layer of complexity to describing the data, conducting the analyses, and reporting the results. Primarily, weighting results in standard errors for each estimate and its proportion. This standard error helps capture the complex survey design elements but makes reporting the results much more challenging. As the point of this article was not to produce national estimates but to demonstrate statistical principles, we chose not to account for weight.

In conclusion, accurately describing data in tables and figure helps to make important decisions on study inclusion criteria, present and convey results to readers, and make decisions regarding which statistical approach is valid. Although the field has previously emphasized including p values in tables, recent advancements have de-emphasized this and, instead, descriptions of data should focus on meaningful differences not just those that may be statistically significant.

Funding Information

Dr. Ho is supported by the Case Western Reserve University Clinical and Translational Science Collaborative of Cleveland (KL2TR002547).

Author Disclosure Statement

Dr. Ho's spouse is a consultant for Zimmer Biomet, Sig Medical, Atricure, and Medtronic.

This publication was made possible by the Clinical and Translational Science Collaborative of Cleveland, KL2TR002547 from the National Center for Advancing Translational Sciences (NCATS) component of the National Institutes of Health and NIH roadmap for Medical Research. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH.

• How Far Trump Would Go

D onald Trump thinks he’s identified a crucial mistake of his first term: He was too nice.

We’ve been talking for more than an hour on April 12 at his fever-dream palace in Palm Beach. Aides lurk around the perimeter of a gilded dining room overlooking the manicured lawn. When one nudges me to wrap up the interview, I bring up the many former Cabinet officials who refuse to endorse Trump this time. Some have publicly warned that he poses a danger to the Republic. Why should voters trust you, I ask, when some of the people who observed you most closely do not?

As always, Trump punches back, denigrating his former top advisers. But beneath the typical torrent of invective, there is a larger lesson he has taken away. “I let them quit because I have a heart. I don’t want to embarrass anybody,” Trump says. “I don’t think I’ll do that again. From now on, I’ll fire.” 

Six months from the 2024 presidential election, Trump is better positioned to win the White House than at any point in either of his previous campaigns. He leads Joe Biden by slim margins in most polls, including in several of the seven swing states likely to determine the outcome. But I had not come to ask about the election, the disgrace that followed the last one, or how he has become the first former—and perhaps future—American President to face a criminal trial . I wanted to know what Trump would do if he wins a second term, to hear his vision for the nation, in his own words.

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What emerged in two interviews with Trump , and conversations with more than a dozen of his closest advisers and confidants, were the outlines of an imperial presidency that would reshape America and its role in the world. To carry out a deportation operation designed to remove more than 11 million people from the country, Trump told me, he would be willing to build migrant detention camps and deploy the U.S. military, both at the border and inland. He would let red states monitor women’s pregnancies and prosecute those who violate abortion bans. He would, at his personal discretion, withhold funds appropriated by Congress, according to top advisers. He would be willing to fire a U.S. Attorney who doesn’t carry out his order to prosecute someone, breaking with a tradition of independent law enforcement that dates from America’s founding. He is weighing pardons for every one of his supporters accused of attacking the U.S. Capitol on Jan. 6, 2021, more than 800 of whom have pleaded guilty or been convicted by a jury. He might not come to the aid of an attacked ally in Europe or Asia if he felt that country wasn’t paying enough for its own defense. He would gut the U.S. civil service, deploy the National Guard to American cities as he sees fit, close the White House pandemic-preparedness office, and staff his Administration with acolytes who back his false assertion that the 2020 election was stolen.

Trump remains the same guy, with the same goals and grievances. But in person, if anything, he appears more assertive and confident. “When I first got to Washington, I knew very few people,” he says. “I had to rely on people.” Now he is in charge. The arranged marriage with the timorous Republican Party stalwarts is over; the old guard is vanquished, and the people who remain are his people. Trump would enter a second term backed by a slew of policy shops staffed by loyalists who have drawn up detailed plans in service of his agenda, which would concentrate the powers of the state in the hands of a man whose appetite for power appears all but insatiable. “I don’t think it’s a big mystery what his agenda would be,” says his close adviser Kellyanne Conway. “But I think people will be surprised at the alacrity with which he will take action.”

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The courts, the Constitution, and a Congress of unknown composition would all have a say in whether Trump’s objectives come to pass. The machinery of Washington has a range of defenses: leaks to a free press, whistle-blower protections, the oversight of inspectors general. The same deficiencies of temperament and judgment that hindered him in the past remain present. If he wins, Trump would be a lame duck—contrary to the suggestions of some supporters, he tells TIME he would not seek to overturn or ignore the Constitution’s prohibition on a third term. Public opinion would also be a powerful check. Amid a popular outcry, Trump was forced to scale back some of his most draconian first-term initiatives, including the policy of separating migrant families. As George Orwell wrote in 1945, the ability of governments to carry out their designs “depends on the general temper in the country.”

Every election is billed as a national turning point. This time that rings true. To supporters, the prospect of Trump 2.0, unconstrained and backed by a disciplined movement of true believers, offers revolutionary promise. To much of the rest of the nation and the world, it represents an alarming risk. A second Trump term could bring “the end of our democracy,” says presidential historian Douglas Brinkley, “and the birth of a new kind of authoritarian presidential order.”

Trump steps onto the patio at Mar-a-Lago near dusk. The well-heeled crowd eating Wagyu steaks and grilled branzino pauses to applaud as he takes his seat. On this gorgeous evening, the club is a MAGA mecca. Billionaire donor Steve Wynn is here. So is Speaker of the House Mike Johnson , who is dining with the former President after a joint press conference proposing legislation to prevent noncitizens from voting. Their voting in federal elections is already illegal, and extremely rare, but remains a Trumpian fixation that the embattled Speaker appeared happy to co-sign in exchange for the political cover that standing with Trump provides.

At the moment, though, Trump’s attention is elsewhere. With an index finger, he swipes through an iPad on the table to curate the restaurant’s soundtrack. The playlist veers from Sinead O’Connor to James Brown to  The Phantom of the Opera.  And there’s a uniquely Trump choice: a rendition of “The Star-Spangled Banner” sung by a choir of defendants imprisoned for attacking the U.S. Capitol on Jan. 6, interspersed with a recording of Trump reciting the Pledge of Allegiance. This has become a staple of his rallies, converting the ultimate symbol of national unity into a weapon of factional devotion. 

The spectacle picks up where his first term left off. The events of Jan. 6 , during which a pro-Trump mob attacked the center of American democracy in an effort to subvert the peaceful transfer of power, was a profound stain on his legacy. Trump has sought to recast an insurrectionist riot as an act of patriotism. “I call them the J-6 patriots,” he says. When I ask whether he would consider pardoning every one of them, he says, “Yes, absolutely.” As Trump faces dozens of felony charges, including for election interference, conspiracy to defraud the United States, willful retention of national-security secrets, and falsifying business records to conceal hush-money payments, he has tried to turn legal peril into a badge of honor.

In a second term, Trump’s influence on American democracy would extend far beyond pardoning powers. Allies are laying the groundwork to restructure the presidency in line with a doctrine called the unitary executive theory, which holds that many of the constraints imposed on the White House by legislators and the courts should be swept away in favor of a more powerful Commander in Chief.

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Nowhere would that power be more momentous than at the Department of Justice. Since the nation’s earliest days, Presidents have generally kept a respectful distance from Senate-confirmed law-enforcement officials to avoid exploiting for personal ends their enormous ability to curtail Americans’ freedoms. But Trump, burned in his first term by multiple investigations directed by his own appointees, is ever more vocal about imposing his will directly on the department and its far-flung investigators and prosecutors.

In our Mar-a-Lago interview, Trump says he might fire U.S. Attorneys who refuse his orders to prosecute someone: “It would depend on the situation.” He’s told supporters he would seek retribution against his enemies in a second term. Would that include Fani Willis , the Atlanta-area district attorney who charged him with election interference, or Alvin Bragg, the Manhattan DA in the Stormy Daniels case, who Trump has previously said should be prosecuted? Trump demurs but offers no promises. “No, I don’t want to do that,” he says, before adding, “We’re gonna look at a lot of things. What they’ve done is a terrible thing.”

Trump has also vowed to appoint a “real special prosecutor” to go after Biden. “I wouldn’t want to hurt Biden,” he tells me. “I have too much respect for the office.” Seconds later, though, he suggests Biden’s fate may be tied to an upcoming Supreme Court ruling on whether Presidents can face criminal prosecution for acts committed in office. “If they said that a President doesn’t get immunity,” says Trump, “then Biden, I am sure, will be prosecuted for all of his crimes.” (Biden has not been charged with any, and a House Republican effort to impeach him has failed to unearth evidence of any crimes or misdemeanors, high or low.)

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Such moves would be potentially catastrophic for the credibility of American law enforcement, scholars and former Justice Department leaders from both parties say. “If he ordered an improper prosecution, I would expect any respectable U.S. Attorney to say no,” says Michael McConnell, a former U.S. appellate judge appointed by President George W. Bush. “If the President fired the U.S. Attorney, it would be an enormous firestorm.” McConnell, now a Stanford law professor, says the dismissal could have a cascading effect similar to the Saturday Night Massacre , when President Richard Nixon ordered top DOJ officials to remove the special counsel investigating Watergate. Presidents have the constitutional right to fire U.S. Attorneys, and typically replace their predecessors’ appointees upon taking office. But discharging one specifically for refusing a President’s order would be all but unprecedented.

Trump’s radical designs for presidential power would be felt throughout the country. A main focus is the southern border. Trump says he plans to sign orders to reinstall many of the same policies from his first term, such as the Remain in Mexico program, which requires that non-Mexican asylum seekers be sent south of the border until their court dates, and Title 42 , which allows border officials to expel migrants without letting them apply for asylum. Advisers say he plans to cite record border crossings and fentanyl- and child-trafficking as justification for reimposing the emergency measures. He would direct federal funding to resume construction of the border wall, likely by allocating money from the military budget without congressional approval. The capstone of this program, advisers say, would be a massive deportation operation that would target millions of people. Trump made similar pledges in his first term, but says he plans to be more aggressive in a second. “People need to be deported,” says Tom Homan, a top Trump adviser and former acting head of Immigration and Customs Enforcement. “No one should be off the table.”

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For an operation of that scale, Trump says he would rely mostly on the National Guard to round up and remove undocumented migrants throughout the country. “If they weren’t able to, then I’d use [other parts of] the military,” he says. When I ask if that means he would override the Posse Comitatus Act—an 1878 law that prohibits the use of military force on civilians—Trump seems unmoved by the weight of the statute. “Well, these aren’t civilians,” he says. “These are people that aren’t legally in our country.” He would also seek help from local police and says he would deny funding for jurisdictions that decline to adopt his policies. “There’s a possibility that some won’t want to participate,” Trump says, “and they won’t partake in the riches.”

As President, Trump nominated three Supreme Court Justices who voted to overturn  Roe v. Wade,  and he claims credit for his role in ending a constitutional right to an abortion. At the same time, he has sought to defuse a potent campaign issue for the Democrats by saying he wouldn’t sign a federal ban. In our interview at Mar-a-Lago, he declines to commit to vetoing any additional federal restrictions if they came to his desk. More than 20 states now have full or partial abortion bans, and Trump says those policies should be left to the states to do what they want, including monitoring women’s pregnancies. “I think they might do that,” he says. When I ask whether he would be comfortable with states prosecuting women for having abortions beyond the point the laws permit, he says, “It’s irrelevant whether I’m comfortable or not. It’s totally irrelevant, because the states are going to make those decisions.” President Biden has said he would fight state anti-abortion measures in court and with regulation.

Trump’s allies don’t plan to be passive on abortion if he returns to power. The Heritage Foundation has called for enforcement of a 19th century statute that would outlaw the mailing of abortion pills. The Republican Study Committee (RSC), which includes more than 80% of the House GOP conference, included in its 2025 budget proposal the Life at Conception Act, which says the right to life extends to “the moment of fertilization.” I ask Trump if he would veto that bill if it came to his desk. “I don’t have to do anything about vetoes,” Trump says, “because we now have it back in the states.”

Presidents typically have a narrow window to pass major legislation. Trump’s team is eyeing two bills to kick off a second term: a border-security and immigration package, and an extension of his 2017 tax cuts. Many of the latter’s provisions expire early in 2025: the tax cuts on individual income brackets, 100% business expensing, the doubling of the estate-tax deduction. Trump is planning to intensify his protectionist agenda, telling me he’s considering a tariff of more than 10% on all imports, and perhaps even a 100% tariff on some Chinese goods. Trump says the tariffs will liberate the U.S. economy from being at the mercy of foreign manufacturing and spur an industrial renaissance in the U.S. When I point out that independent analysts estimate Trump’s first term tariffs on thousands of products, including steel and aluminum, solar panels, and washing machines, may have cost the U.S. $316 billion and more than 300,000 jobs, by one account, he dismisses these experts out of hand. His advisers argue that the average yearly inflation rate in his first term—under 2%—is evidence that his tariffs won’t raise prices.

Since leaving office, Trump has tried to engineer a caucus of the compliant, clearing primary fields in Senate and House races. His hope is that GOP majorities replete with MAGA diehards could rubber-stamp his legislative agenda and nominees. Representative Jim Banks of Indiana, a former RSC chairman and the GOP nominee for the state’s open Senate seat, recalls an August 2022 RSC planning meeting with Trump at his residence in Bedminster, N.J. As the group arrived, Banks recalls, news broke that Mar-a-Lago had been raided by the FBI. Banks was sure the meeting would be canceled. Moments later, Trump walked through the doors, defiant and pledging to run again. “I need allies there when I’m elected,” Banks recalls Trump saying. The difference in a second Trump term, Banks says now, “is he’s going to have the backup in Congress that he didn’t have before.”

Trump’s intention to remake America’s relations abroad may be just as consequential. Since its founding, the U.S. has sought to build and sustain alliances based on the shared values of political and economic freedom. Trump takes a much more transactional approach to international relations than his predecessors, expressing disdain for what he views as free-riding friends and appreciation for authoritarian leaders like President Xi Jinping of China, Prime Minister Viktor Orban of Hungary, or former President Jair Bolsonaro of Brazil.

That’s one reason America’s traditional allies were horrified when Trump recently said at a campaign rally that Russia could “do whatever the hell they want” to a NATO country he believes doesn’t spend enough on collective defense. That wasn’t idle bluster, Trump tells me. “If you’re not going to pay, then you’re on your own,” he says. Trump has long said the alliance is ripping the U.S. off. Former NATO Secretary-General Jens Stoltenberg credited Trump’s first-term threat to pull out of the alliance with spurring other members to add more than $100 billion to their defense budgets.

But an insecure NATO is as likely to accrue to Russia’s benefit as it is to America’s. President Vladimir Putin’s 2022 invasion of Ukraine looks to many in Europe and the U.S. like a test of his broader vision to reconstruct the Soviet empire. Under Biden and a bipartisan Congress, the U.S. has sent more than $100 billion to Ukraine to defend itself. It’s unlikely Trump would extend the same support to Kyiv. After Orban visited Mar-a-Lago in March, he said Trump “wouldn’t give a penny” to Ukraine. “I wouldn’t give unless Europe starts equalizing,” Trump hedges in our interview. “If Europe is not going to pay, why should we pay? They’re much more greatly affected. We have an ocean in between us. They don’t.” (E.U. nations have given more than $100 billion in aid to Ukraine as well.)

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Trump has historically been reluctant to criticize or confront Putin. He sided with the Russian autocrat over his own intelligence community when it asserted that Russia interfered in the 2016 election. Even now, Trump uses Putin as a foil for his own political purposes. When I asked Trump why he has not called for the release of Wall Street Journal reporter Evan Gershkovich, who has been unjustly held on spurious charges in a Moscow prison for a year , Trump says, “I guess because I have so many other things I’m working on.” Gershkovich should be freed, he adds, but he doubts it will happen before the election. “The reporter should be released and he will be released,” Trump tells me. “I don’t know if he’s going to be released under Biden. I would get him released.”

America’s Asian allies, like its European ones, may be on their own under Trump. Taiwan’s Foreign Minister recently said aid to Ukraine was critical in deterring Xi from invading the island. Communist China’s leaders “have to understand that things like that can’t come easy,” Trump says, but he declines to say whether he would come to Taiwan’s defense. 

Trump is less cryptic on current U.S. troop deployments in Asia. If South Korea doesn’t pay more to support U.S. troops there to deter Kim Jong Un’s increasingly belligerent regime to the north, Trump suggests the U.S. could withdraw its forces. “We have 40,000 troops that are in a precarious position,” he tells TIME. (The number is actually 28,500.) “Which doesn’t make any sense. Why would we defend somebody? And we’re talking about a very wealthy country.”

Transactional isolationism may be the main strain of Trump’s foreign policy, but there are limits. Trump says he would join Israel’s side in a confrontation with Iran. “If they attack Israel, yes, we would be there,” he tells me. He says he has come around to the now widespread belief in Israel that a Palestinian state existing side by side in peace is increasingly unlikely. “There was a time when I thought two-state could work,” he says. “Now I think two-state is going to be very, very tough.”

Yet even his support for Israel is not absolute. He’s criticized Israel’s handling of its war against Hamas, which has killed more than 30,000 Palestinians in Gaza, and has called for the nation to “get it over with.” When I ask whether he would consider withholding U.S. military aid to Israel to push it toward winding down the war, he doesn’t say yes, but he doesn’t rule it out, either. He is sharply critical of Israeli Prime Minister Benjamin Netanyahu, once a close ally. “I had a bad experience with Bibi,” Trump says. In his telling, a January 2020 U.S. operation to assassinate a top Iranian general was supposed to be a joint attack until Netanyahu backed out at the last moment. “That was something I never forgot,” he says. He blames Netanyahu for failing to prevent the Oct. 7 attack, when Hamas militants infiltrated southern Israel and killed nearly 1,200 people amid acts of brutality including burning entire families alive and raping women and girls. “It happened on his watch,” Trump says.

On the second day of Trump’s New York trial on April 17, I stand behind the packed counter of the Sanaa Convenience Store on 139th Street and Broadway, waiting for Trump to drop in for a postcourt campaign stop. He chose the bodega for its history. In 2022, one of the store’s clerks fatally stabbed a customer who attacked him. Bragg, the Manhattan DA, charged the clerk with second-degree murder. (The charges were later dropped amid public outrage over video footage that appeared to show the clerk acting in self-defense.) A baseball bat behind the counter alludes to lingering security concerns. When Trump arrives, he asks the store’s co-owner, Maad Ahmed, a Yemeni immigrant, about safety. “You should be allowed to have a gun,” Trump tells Ahmed. “If you had a gun, you’d never get robbed.”

On the campaign trail, Trump uses crime as a cudgel, painting urban America as a savage hell-scape even though violent crime has declined in recent years, with homicides sinking 6% in 2022 and 13% in 2023, according to the FBI. When I point this out, Trump tells me he thinks the data, which is collected by state and local police departments, is rigged. “It’s a lie,” he says. He has pledged to send the National Guard into cities struggling with crime in a second term—possibly without the request of governors—and plans to approve Justice Department grants only to cities that adopt his preferred policing methods like stop-and-frisk.

To critics, Trump’s preoccupation with crime is a racial dog whistle. In polls, large numbers of his supporters have expressed the view that antiwhite racism now represents a greater problem in the U.S. than the systemic racism that has long afflicted Black Americans. When I ask if he agrees, Trump does not dispute this position. “There is a definite antiwhite feeling in the country,” he tells TIME, “and that can’t be allowed either.” In a second term, advisers say, a Trump Administration would rescind Biden’s Executive Orders designed to boost diversity and racial equity.

Trump’s ability to campaign for the White House in the midst of an unprecedented criminal trial is the product of a more professional campaign operation that has avoided the infighting that plagued past versions. “He has a very disciplined team around him,” says Representative Elise Stefanik of New York. “That is an indicator of how disciplined and focused a second term will be.” That control now extends to the party writ large. In 2016, the GOP establishment, having failed to derail Trump’s campaign, surrounded him with staff who sought to temper him. Today the party’s permanent class have either devoted themselves to the gospel of MAGA or given up. Trump has cleaned house at the Republican National Committee, installing handpicked leaders—including his daughter-in-law—who have reportedly imposed loyalty tests on prospective job applicants, asking whether they believe the false assertion that the 2020 election was stolen. (The RNC has denied there is a litmus test.) Trump tells me he would have trouble hiring anyone who admits Biden won: “I wouldn’t feel good about it.”

Policy groups are creating a government-in-waiting full of true believers. The Heritage Foundation’s Project 2025 has drawn up plans for legislation and Executive Orders as it trains prospective personnel for a second Trump term. The Center for Renewing America, led by Russell Vought, Trump’s former director of the Office of Management and Budget, is dedicated to disempowering the so-called administrative state, the collection of bureaucrats with the power to control everything from drug-safety determinations to the contents of school lunches. The America First Policy Institute is a research haven of pro-Trump right-wing populists. America First Legal, led by Trump’s immigration adviser Stephen Miller, is mounting court battles against the Biden Administration. 

The goal of these groups is to put Trump’s vision into action on day one. “The President never had a policy process that was designed to give him what he actually wanted and campaigned on,” says Vought. “[We are] sorting through the legal authorities, the mechanics, and providing the momentum for a future Administration.” That includes a litany of boundary-pushing right-wing policies, including slashing Department of Justice funding and cutting climate and environmental regulations.

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Trump’s campaign says he would be the final decision-maker on which policies suggested by these organizations would get implemented. But at the least, these advisers could form the front lines of a planned march against what Trump dubs the Deep State, marrying bureaucratic savvy to their leader’s anti-bureaucratic zeal. One weapon in Trump’s second-term “War on Washington” is a wonky one: restoring the power of impoundment, which allowed Presidents to withhold congressionally appropriated funds. Impoundment was a favorite maneuver of Nixon, who used his authority to freeze funding for subsidized housing and the Environmental Protection Agency. Trump and his allies plan to challenge a 1974 law that prohibits use of the measure, according to campaign policy advisers.

Another inside move is the enforcement of Schedule F, which allows the President to fire nonpolitical government officials and which Trump says he would embrace. “You have some people that are protected that shouldn’t be protected,” he says. A senior U.S. judge offers an example of how consequential such a move could be. Suppose there’s another pandemic, and President Trump wants to push the use of an untested drug, much as he did with hydroxychloroquine during COVID-19. Under Schedule F, if the drug’s medical reviewer at the Food and Drug Administration refuses to sign off on its use, Trump could fire them, and anyone else who doesn’t approve it. The Trump team says the President needs the power to hold bureaucrats accountable to voters. “The mere mention of Schedule F,” says Vought, “ensures that the bureaucracy moves in your direction.”

It can be hard at times to discern Trump’s true intentions. In his interviews with TIME, he often sidestepped questions or answered them in contradictory ways. There’s no telling how his ego and self-destructive behavior might hinder his objectives. And for all his norm-breaking, there are lines he says he won’t cross. When asked if he would comply with all orders upheld by the Supreme Court, Trump says he would. 

But his policy preoccupations are clear and consistent. If Trump is able to carry out a fraction of his goals, the impact could prove as transformative as any presidency in more than a century. “He’s in full war mode,” says his former adviser and occasional confidant Stephen Bannon. Trump’s sense of the state of the country is “quite apocalyptic,” Bannon says. “That’s where Trump’s heart is. That’s where his obsession is.”

These obsessions could once again push the nation to the brink of crisis. Trump does not dismiss the possibility of political violence around the election. “If we don’t win, you know, it depends,” he tells TIME. “It always depends on the fairness of the election.” When I ask what he meant when he baselessly claimed on Truth Social that a stolen election “allows for the termination of all rules, regulations and articles, even those found in the Constitution,” Trump responded by denying he had said it. He then complained about the “Biden-inspired” court case he faces in New York and suggested that the “fascists” in America’s government were its greatest threat. “I think the enemy from within, in many cases, is much more dangerous for our country than the outside enemies of China, Russia, and various others,” he tells me.

Toward the end of our conversation at Mar-a-Lago, I ask Trump to explain another troubling comment he made: that he wants to be dictator for a day. It came during a Fox News town hall with Sean Hannity, who gave Trump an opportunity to allay concerns that he would abuse power in office or seek retribution against political opponents. Trump said he would not be a dictator—“except for day one,” he added. “I want to close the border, and I want to drill, drill, drill.”

Trump says that the remark “was said in fun, in jest, sarcastically.” He compares it to an infamous moment from the 2016 campaign, when he encouraged the Russians to hack and leak Hillary Clinton’s emails. In Trump’s mind, the media sensationalized those remarks too. But the Russians weren’t joking: among many other efforts to influence the core exercise of American democracy that year, they hacked the Democratic National Committee’s servers and disseminated its emails through WikiLeaks.

Whether or not he was kidding about bringing a tyrannical end to our 248-year experiment in democracy, I ask him, Don’t you see why many Americans see such talk of dictatorship as contrary to our most cherished principles? Trump says no. Quite the opposite, he insists. “I think a lot of people like it.” — With reporting by Leslie Dickstein, Simmone Shah, and Julia Zorthian

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U.S. women's basketball team beats France by 1 point to get 8th straight Olympic gold medal

Updated on: August 11, 2024 / 12:15 PM EDT / CBS/AP

The U.S. women's basketball team won its straight 8th Olympic gold medal, beating host France by the tightest of margins: 1 point. Team USA won 67 to 66 in a contested final match that came down to the last shot.

Led by A'ja Wilson, who scored 21 points, the U.S. survived a last-second shot by Gabby Williams that was just inside the 3-point line to hold off France.

No team had been able to push the Americans during this impressive streak of 61 consecutive wins. The win was the closest the U.S. has ever won an Olympic gold medal since the 1988 Games when they beat Yugoslavia by seven points. The only other team to keep the U.S. at single digits in a gold medal game was South Korea at the 1984 Games.

"It's amazing. It truly is a dynasty that we have built here at USAB has been incredible," Wilson said. "And I am so proud of the resilience that my team showed. We could have fumbled it many times, but we pulled through. To say I am a two-time gold medalist, I am so blessed."

With Sunday's victory, the U.S. women's legacy stretches to 61 consecutive wins in Olympic contests. It also breaks a tie with the U.S. men's program that won seven in a row from 1936-68.

The women's victory came fewer than 24 hours after the U.S. men's team  also beat France in the title game. This was the first time in Olympic history that both gold medal games featured the same two teams.

Unlike the men's game, this one came down to the final minute and one last shot by France that was just inside the 3-point line.

The Americans were up 67-64 with 3.9 seconds left after Kahleah Copper hit two free throws. Marine Johannes brought the ball up the court to Williams and the former UConn standout caught the ball just inside the 3-point line and banked in over the outstretched arms of Breanna Stewart for the final margin.

There was a brief delay before the officials signaled that it was a two-point shot, which led to the beginning of a celebration and a lot of happy hugs for the Americans and left the French players standing in disbelief after falling just short.

"Gabby hit some great shots down the end, tough shots," Wilson said. "We understood what we had in our locker room and leaning on each other and talking to one another and believing that we believed in each other and that's the greatest thing about it."

The American players went to celebrate with the celebrities sitting courtside including men's basketball players LeBron James, Bam Adebayo, Derrick White, along with U.S. women's greats Lisa Leslie, Sue Bird and Dawn Staley.

Williams, who finished with 19 points, had hit a deep 3 a few seconds earlier to get France within one before Copper's free throws. She got a consoling hug from Staley.

The victory gave Diana Taurasi a sixth consecutive gold medal, making her the most decorated basketball player in Olympic history, breaking a tie with longtime teammate Sue Bird, who won five.

Taurasi, who didn't play in the gold medal game, has been humble about the potential record, saying she cares more about the team winning than her individual success.

It's been a trying Olympics for her as she didn't start any of the knockout phase games, the first time she wasn't in the opening lineup since the 2004 Olympics.

• Women's Basketball

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