representation of data class 5

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Grade 5 Data and Graphing Worksheets

Introducing statistics.

Our  grade 5 data and graphing exercises extend previous graphing skills (double bar and line graphs, line plots and circle graphs with fractions) and introduce basic probability and statistics (range, mode, mean, median).

Grade 5 data and graphing worksheet

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5th Grade Data Handling Worksheet

In 5th grade data handling worksheet, students can practice the questions on bar graph, line graph and pie chart. We represent the data in many ways. A graph is a pictorial representation of information. In pictograph the information is presented by using a picture as symbol. Bar graph is a method of presenting information by drawing rectangular bars of equal width and with equal space between the bars.

1. Choose the right answer to show the type of graph that will be used for the following information.

I. Number of students in the 5 sections of Grade 5.

(i) Double Bar graph                 (ii) Bar Graph

II. Favorite color of the students of class 5.

(i) Bar graph                           (ii) Line Graph

III. The sale of product of a company in last 6 months.

(i) Pictograph                          (ii) Line Graph

IV. Marks obtained by Michael in different objects in 2 terms of the year.

(i) Double Bar graph                (ii) Bar Graph

2. The face of the clock is like a pie chart with 12 parts. Then:

(i) What is the angle of each part?

(ii) How many hours will represent \(\frac{1}{3}\) of the Pie Chart?

3. Given below is the amount of money withdrawn by Mr Matthew from his bank account in last 6 months. Tick the most suitable scale to be used for making a Bar Graph.

(i) $ 1,00,000         (ii) $ 70,000          (iii) $ 25,000         (iv) $ 50,000

4. Tick the right Pie Chart for the given information.

5. Fill in the blanks.

(i) _________ graph is suitable when we need to compare data elements.

(ii) _________ is a collection of numbers gathered to give some meaningful information.

(iii) A __________ represents data through pictures of objects.

(iv) On the scale of 1 unit length = 5 kg, the bar of length 7 units will represent _______ kg.

(v) __________ graphs are used to show change or trend over time.

6. Observe the double bar graph given below and answer the questions.

(i) How many students are there in grade 1 in the year 2018?

(ii) What was the least strength of Grade 2 in the given four years?

(iii) What was the difference in the strength of Grade 1 and 2 in the years 2016?

(iv) In which year the difference in the strength of both the grades was maximum?

7. Number of cars sold by a dealer in a week is given below. Draw a line graph for the given data.

8. 48 students were surveyed to find out about their favorite drink. The information collected has been tabulated. Observe the given data and draw a pie chart.

Answer the given questions.

(i) Which is the most favorite drink of the students?

(ii) How many more students like Lemonade than Apple Juice?

(iii) Which is your favorite drink?

  1.  I.   (ii) Bar Graph

II.   (i) Bar graph 

III.    (ii) Line Graph

IV.   (i) Double Bar graph

2.  (i) 30

(ii) 4 hours

3.    (iii) $ 25,000  

(iii) Pictograph

8. (i) Fresh Fruit Juice

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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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Class Notes NCERT Solutions for CBSE Students

NCERT 5th Class (CBSE) Mathematics: Graphical Representation

admin April 5, 2018 5th Class , Mathematics 4,478 Views

PICTOGRAPHS

• Pictograph use pictures or symbols to represent information.
• It has a title.
• It gives the definition of the symbol or the key. The key is defined such that it represents the entire data.
• pictographs help you understand the information by allowing you to compare the data shown.

(a) The table shows the number of magazines published for children.

This pictograph shows the same information.

(b) Represent the following information in the form of a pictograph. Give the pictograph a title and show what your symbol stands for

Favorite TV channels in Class V:

Comedy – 15 children, Cartoons – 25 children, Sports – 10 children, Adventure – 5 children.

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Smart Charts Class 5 Notes CBSE Maths Chapter 12 (Free PDF Download)

• Revision Notes
• Chapter 12 Smart Charts

Learn How to Make Smart Charts with CBSE Class 5 Maths Chapter 12 Revision Notes

Embark on an exciting exploration in Class 5 Maths Chapter 12 - 'Smart Charts.' This chapter makes learning about data representation enjoyable and accessible, introducing students to the world of charts. Explore the fundamentals of creating and interpreting charts, laying the groundwork for effective data analysis. In Class 5, where students encounter diverse mathematical concepts, Smart Chart revision notes by Vedantu's expert teachers prove invaluable, offering comprehensive study material with clear explanations.

The revision notes will cover all the aspects of this chapter including making colourful charts from available information. You will find learning how to extract information from pictorial representations becomes easier. Get these free Smart Chart revision files today and get started with your preparation.

Download CBSE Class 4 EVS Revision Notes 2023-24 PDF

Access Class 5 Mathematics Chapter 12- Smart Charts

Summary of “smart charts”.

This chapter aims to make us understand the importance of tables and charts.

There are mainly five different types of smart charts:

Tally Marks

Tabular Forms

Family Tree

Tally Marks are used to keep track of numbers as quickly as possible. 

Tally marks are used for counting and are shown as a set of five lines, four vertical lines (one vertical line for each of the first four numbers), and a diagonal line across the preceding four numbers.

Let’s See Tally Marks To Understand It More Clearly:

For each of the four counts, we added a vertical line (|). 

For the fifth count, a diagonal line (/) is added. Tally markings can be seen here.

Tally Marks for the Number of Animals

A presentation of information or data called a table is usually made up of rows and columns. However, it may sometimes have a more sophisticated structure. 

Tables consist of two major parts, i.e. Rows and Columns.

A column is vertical in alignment, whereas a row is horizontal. 

Tables are frequently used in data analysis, research, and communication.

Below table has 5 columns and 4 rows. Using this table, we can easily understand the number of males and females in each game.

A pie chart is a sort of chart that shows data in a circular graph. 

It is one of the most often used graphs for representing data by combining the qualities of circles to reflect real-world information. 

A pie chart is circular, with the pie representing the entire data and the slice out of the pie representing the parts of the data and recording it individually.

Let us look at the following example of the following pie chart that represents the different percentages for each slice.

Example: The following pie chart represents the number of students in class with their favorite sports:

Cricket: 37%

Football: 25%

BasketBall: 22%

Volleyball: 16%

A visual way to compare quantitative data using rectangles whose lengths are proportionate to the quantity of the data or items being compared; also known as a bar chart.

Family Tree 

A family tree is a graphical or visual representation of our ancestors. 

A Family Tree

Solved Examples

Temperature Graph

Find Out From the Bar Chart:

1. Which city is hottest on 1 June?

Ans: Jaisalmer is hottest on 1 June

2. Which city is coldest on 1 December?

Ans: Shimla is coldest on 1 December

3. Which city shows little change in temperature on the two days ----1 June and 1 December?

Ans: Bangalore shows little change in temperature on the two days. Lowest change = 28 – 24 = 4 degree Celcius.

Q1. Ajay made a record of his favourite animals he saw in the zoo. Make a tally chart and answer the following questions.

Tally Chart

Q 1. How many Tigers are there?

Q 2. What is the difference between the number of tigers and elephants?

Q 3. Which is more Giraffe or Lion?

Q 4. How many animals in total did Ajay see?

Q 2. Given below is the representation of different vehicles in a town. Study and answer the questions. (1 ☆ = 10 vehicles)

Number of Vehicles in a Town

(a) Which vehicle is the maximum in town?

(b) Which vehicle is 50 in number?

(c) What is the total number of vehicles in the town?

Ans: a) Motobike

         b) Car

         c) 360 

Tricks for Student:

Check your work at the end, as most of the questions are based on counting any representation and calculating it. So after doing the calculation, check it again.

While drawing a graph, always take care of the scale and ratio of the graph. 

Always keep in mind the hierarchy while making the family tree.

Importance of CBSE Class 5 Chapter 12 Smart Charts

The syllabus of Class 5 Maths is unique in terms of creating a conceptual foundation of various mathematical concepts. The importance of Chapter 12 can be understood from the following points.

Understanding the difference between rows and columns

Creating a conceptual foundation for making tables by including rows and columns

Learning how to figure out information from a given table and answering questions

Perfect way of delivering knowledge with pictures

Reading information from words and pictures simultaneously and answering questions

Understanding the type, similarity, dissimilarity, and eligibility of data in simpler versions to introduce in a particular table

Studying Smart Charts Class 5 will help make students better in thinking logically and solving problems accordingly. It is formulated to create a strong foundation for formulating tables, using data, and extracting information. Hence, the students will be introduced to the basic level of statistics at a young age.

Benefits of Vedantu’s Maths Chart for Class 5 Revision Notes

Now that you have understood the importance of this chapter, here is how Vedantu can deliver the best results with its revision notes and worksheets.

Learning What is Smart Chart

As mentioned earlier, you will learn the definition and use of smart charts for the first time in Class 5. The revision notes for this chapter will be the ideal study material to refer to grab hold of the concept.

Quick Resolution of Doubts

All the doubts rising in your mind can be resolved by using the simpler explanation of concepts in these revision notes.

A Basic Introduction to Statistics

Children will also get excellent support in studying these basic concepts related to statistics and other advanced mathematical operations. They will learn how to input data in charts for objects, things, activities such as dice throwing, etc.

Learning to Identify and Differentiate Objects

The revision notes will also help you by getting smart with charts. Learn how to differentiate between various objects and their eligibility.

Getting Smart with Charts Has Become Easier

NCERT Solutions plays a crucial role in Class 6 exam prep. Start by thoroughly reading the textbook chapter. After that, solve the NCERT questions for Class 5 Chapter 12 - Smart Charts. You can find detailed solutions on Vedantu, aligning with CBSE guidelines. Download the free NCERT Solutions for Class 5 Chapter 12 - Smart Charts to guide your exam preparation with expert-reviewed answers. Download the revision notes today for free and check what we see on the road. Prepare the answers in the best way possible to save time and score better in the exams. Visit our website to download the PDFs for free and find other related study materials.

FAQs on Smart Charts Class 5 Notes CBSE Maths Chapter 12 (Free PDF Download)

1. Why is getting Smart with Charts easier with Vedantu?

The experts compile answers and explain concepts of Maths chapters using a simpler language. They also follow the CBSE guidelines to ensure the explanation matches the standard of the Class 5 students.

2. How can you use revision notes to make smart charts?

Experts will explain how to make tables using the information embedded in the pictures. Focus on making tables. You will also learn how to answer questions based on the Smart Charts summary.

3. How can I prepare Chapter 12 smart charts before an exam?

The preparation of Chapter 12 Smart Charts becomes easier with Vedantu’s revision notes and worksheets. Practice worksheets and take a glance at the concepts in the notes before an exam.

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Graphical Representation of Data

5th Class Mathematics Graphical Representation of Data

Category : 5th Class

Introduction

You might have seen in the books, newspaper etc, graphs are used to give some valuable information, like people living under poverty line in different states, number of mal- nutritioned child in different Asian countries, number of unemployed people in India, number of uneducated people in a particular state etc. In this chapter we will study about the data and analysis of data with the help of graph.

The information, which is in the numeral form, is called data. The data is gathered in various ways. Then it is manipulated and represented on the graph.

The initial data that the observer collects himself is called raw data.

Grouped Data

When raw data is arranged in a table in order to extract the information contained by it easily, is called grouped data.

Presentation of Data

Data is presented with the help of different types of graphs, which are as follows.

When the data is represented on the graph with the help of pictures, it is known as Pictograph.

In the following pictograph, number of students who are present in different classes has been shown:

Key: One boy represents 8 students.

(a) How many students were present in class III?

(b) In which class least number of students were present?

(c) How many students were present in class IV and class V together?

(d) How many more students was present in class IV in comparison of class III

(a) 16                               (b) Class III

(c) 64                               (d) 24

When the data is represented on the graph with the help of bars, it is known as Bargraph.

In the following bar graph, number of fans sold by a shop during a week has been shown.

(a) How many fans were sold by the shop during the week?

(b) On which day, maximum number of fans were sold?

(c) How many more fans were sold on Wednesday in comparison to Tuesday?

(d) On which day 400 fans were sold?

(b) Wednesday

(d) Saturday

Other Topics

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Notes - Graphical Representation of Data

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Graphical Representation of Data

Graphical Representation of Data: Graphical Representation of Data,” where numbers and facts become lively pictures and colorful diagrams . Instead of staring at boring lists of numbers, we use fun charts, cool graphs, and interesting visuals to understand information better. In this exciting concept of data visualization, we’ll learn about different kinds of graphs, charts, and pictures that help us see patterns and stories hidden in data.

There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics .

The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, Astro statistics, and so on . In this article, we have provided everything about the graphical representation of data, including its types, rules, advantages, etc.

Table of Content

What is Graphical Representation

Types of graphical representations, line graphs, histograms , stem and leaf plot , box and whisker plot .

• Graphical Representations used in Maths

Value-Based or Time Series Graphs 

Frequency based, principles of graphical representations, advantages and disadvantages of using graphical system, general rules for graphical representation of data, frequency polygon, solved examples on graphical representation of data.

Graphics Representation is a way of representing any data in picturized form . It helps a reader to understand the large set of data very easily as it gives us various data patterns in visualized form.

There are two ways of representing data,

• Pictorial Representation through graphs.

They say, “A picture is worth a thousand words”.  It’s always better to represent data in a graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in the form of visuals as Human beings process data better in visual form than any other form.

Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time.

Check: Graph and its representations

Comparison between different items is best shown with graphs, it becomes easier to compare the crux of the data about different items. Let’s look at all the different types of graphical representations briefly: 

A line graph is used to show how the value of a particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data and predicting further trends. 

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars. 

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range. 

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point.  

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4).  

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data. 

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole. 

Graphical Representations used in Math’s

Graphs in Math are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths: 

• Value-Based or Time Series Graphs

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values. 

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study.

Also read: Types of Statistical Data

• All types of graphical representations follow algebraic principles.
• When plotting a graph, there’s an origin and two axes.
• The x-axis is horizontal, and the y-axis is vertical.
• The axes divide the plane into four quadrants.
• The origin is where the axes intersect.
• Positive x-values are to the right of the origin; negative x-values are to the left.
• Positive y-values are above the x-axis; negative y-values are below.

• It gives us a summary of the data which is easier to look at and analyze.
• It saves time.
• We can compare and study more than one variable at a time.

Disadvantages

• It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data. 
• Interpretation of graphs can vary based on individual perspectives, leading to subjective conclusions.
• Poorly constructed or misleading visuals can distort data interpretation and lead to incorrect conclusions.

Check : Diagrammatic and Graphic Presentation of Data

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs: 

• Whenever possible, the data source must be mentioned for the viewer.
• Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
• The measurement Unit should be mentioned in the top right corner of the graph.
• The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
• Last but not the least, a suitable title should be chosen.

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval. 

Question 1: What are different types of frequency-based plots? 

Types of frequency-based plots:  Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels. 

Draw a bar graph for the following data. 

• Put each of the channels on the x-axis
• The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following data 

• Put each of the x-axis row value on the x-axis
• joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data: 

• Draw the class intervals on the x-axis and frequencies on the y-axis.
• Calculate the midpoint of each class interval.

Now join the mid points of the intervals and their corresponding frequencies on the graph. 

This graph shows both the histogram and frequency polygon for the given distribution.

Related Article:

Graphical Representation of Data| Practical Work in Geography Class 12 What are the different ways of Data Representation What are the different ways of Data Representation? Charts and Graphs for Data Visualization

Conclusion of Graphical Representation

Graphical representation is a powerful tool for understanding data, but it’s essential to be aware of its limitations. While graphs and charts can make information easier to grasp, they can also be subjective, complex, and potentially misleading . By using graphical representations wisely and critically, we can extract valuable insights from data, empowering us to make informed decisions with confidence.

Graphical Representation of Data – FAQs

What are the advantages of using graphs to represent data.

Graphs offer visualization, clarity, and easy comparison of data, aiding in outlier identification and predictive analysis.

What are the common types of graphs used for data representation?

Common graph types include bar, line, pie, histogram, and scatter plots , each suited for different data representations and analysis purposes.

How do you choose the most appropriate type of graph for your data?

Select a graph type based on data type, analysis objective, and audience familiarity to effectively convey information and insights.

How do you create effective labels and titles for graphs?

Use descriptive titles, clear axis labels with units, and legends to ensure the graph communicates information clearly and concisely.

How do you interpret graphs to extract meaningful insights from data?

Interpret graphs by examining trends, identifying outliers, comparing data across categories, and considering the broader context to draw meaningful insights and conclusions.

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• Diagrammatic Representation of Data

Suppose you are interested to compare the marks of your mates in a test. How can you make the comparison interesting? It can be done by the diagrammatic representations of data. You can use a bar diagram, histograms, pie-charts etc for this.  You will be able to answer questions like –

How will you find out the number of students in the various categories of marks in a certain test? What can you say about the marks obtained by the maximum students? Also, how can you compare the marks of your classmates in five other tests? Is it possible for you to remember the marks of each and every student in all subjects? No! Also, you don’t have the time to compare the marks of every student. Merely noting down the marks and doing comparisons is not interesting at all. Let us study them in detail.

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Bar diagram.

This is one of the simplest techniques to do the comparison for a given set of data. A bar graph is a graphical representation of the data in the form of rectangular bars or columns of equal width. It is the simplest one and easily understandable among the graphs by a group of people.

Browse more Topics under Statistical Description Of Data

• Introduction to Statistics
• Textual and Tabular Representation of Data
• Frequency Distribution
• Frequency Polygon  
• Cumulative Frequency Graph or Ogive

Construction of a Bar Diagram

• Draw two perpendicular lines intersecting each other at a point O. The vertical line is the y-axis and the horizontal is the x-axis.
• Choose a suitable scale to determine the height of each bar.
• On the horizontal line, draw the bars at equal distance with corresponding heights.
• The space between the bars should be equal.

Properties of a Bar Diagram

• Each bar or column in a bar graph is of equal width.
• All bars have a common base.
• The height of the bar corresponds to the value of the data.
• The distance between each bar is the same.

Types of Bar Diagram

A bar graph can be either vertical or horizontal depending upon the choice of the axis as the base. The horizontal bar diagram is used for qualitative data. The vertical bar diagram is used for the quantitative data or time series data. Let us take an example of a bar graph showing the comparison of marks of a student in all subjects out of 100 marks for two tests.

With the bar graph, we can also compare the marks of students in each subject other than the marks of one student in every subject. Also, we can draw the bar graph for every student in all subjects.

We can use another way of diagrammatical representation of data. If we are working with a continuous data set or grouped dataset, we can use a histogram for the representation of data.

• A histogram is similar to a bar graph except for the fact that there is no gap between the rectangular bars. The rectangular bars show the area proportional to the frequency of a variable and the width of the bars represents the class width or class interval.
• Frequency means the number of times a variable is occurring or is present. It is an area graph. The heights of the rectangles are proportional to the corresponding frequencies of similar classes.

Construction of Histogram

• Choose a suitable scale for both the axes to determine the height and width of each bar
• On the horizontal line, draw the bars with corresponding heights
• There should be no gap between two consecutive bars showing the continuity of the data
• If the grouped frequencies are not continuous, the first thing to do is to make them continuous

It is done by adding the average of the difference between the lower limit of the class interval and the upper limit of the preceding class width to the upper limits of all the classes. The same quantity is subtracted from the lower limits of the classes.

Properties of Histogram

• Each bar or column in a bar graph is of equal width and corresponds to the equal class interval
• If the classes are of unequal width then the height of the bars will be proportional to the ration of the frequencies to the width of the classes
• All bars have a common base
• The height of the bar corresponds to the frequency of the data

Suppose we have a data set showing the marks obtained out of 100 by a group of 35 students in statistics. We can find the number of students in the various marks category with the help of the histogram.

A line graph is a type of chart or graph which shows information when a series of data is joined by a line. It shows the changes in the data over a period of time. In a simple line graph, we plot each pair of values of (x, y). Here, the x-axis denotes the various time point (t), and the y-axis denotes the observation based on the time.

Properties of a Line Graph

• It consists of Vertical and Horizontal scales. These scales may or may not be uniform.
• Data point corresponds to the change over a period of time.
• The line joining these data points shows the trend of change.

Below is the line graph showing the number of buses passing through a particular street over a period of time:

Solved Examples for diagrammatic Representation of Data

Problem 1: Draw the histogram for the given data.

Solution: This grouped frequency distribution is not continuous. We need to convert it into a continuous distribution with exclusive type classes. This is done by averaging the difference of the lower limit of one class and the upper limit of the preceding class. Here, d = ½ (19 – 18) = ½ = 0.5. We add 0.5 to all the upper limits and we subtract 0.5 from all the lower limits.

The corresponding histogram is

Draw a line graph for the production of two types of crops for the given years.

Solution: The required graph is

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Learn Class 5 Math - Data Handling

Do you know how you can record the favorite colors of your classmates? This can be only through Data handling. It is used to record and analyse the information of the people. Every class 5 student should be aware of concepts of Data handling and how you can record and present the data.

Let's discuss Data handling and its types.

Data handling

Data handling is defined as the process through which you can gather present and record information in the form of graphs or charts. You can also use the concept of Data handling in finding the Mean, Median and Mode, which is useful in both Maths and Science.

Data are usually organised in charts or graphs for analysis, including facts, measurements, and numbers.

Representation of Data Handling

Data can be organised into different types:

• Stem and Leaf Plots
• Cumulative Tables and graphs
• Frequency Distribution

Examples of Data handling

There are several examples of Data handling that you will face daily in your school and normal life.

Some examples of Data handling that you will find in your classrooms:

• You can use the concept of data handling to determine the remaining stock of chocolates left after chocolate got distributed among the students.
• Through Data handling, you can manage the number of boys and girls present in the class by forming a pie chart.
• You can draw a bar chart to evaluate the hobbies of the present in class.

Some of the basic examples of data handling in real life are:

• The National Census
• Voter Polls
• Online Marketing Surveys

Learning Videos for 5th Grade Math - Data Handling

Data handling sample questions for class 5.

• Number names and Number Sense (7 and 8 digit numbers)
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• Measurement of Length
• Temperature and Money
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• Perimeter of Various Shapes & Area of Rectangle and Square
• Data Handling
• Level 2 & Achievers
• General Knowledge

Module 11: Statistics: Describing Data

Representing data graphically, learning outcomes.

• Create a frequency table, bar graph, pareto chart, pictogram, or a pie chart to represent a data set
• Identify features of ineffective representations of data
• Create a histogram, pie chart, or frequency polygon that represents numerical data
• Create a graph that compares two quantities

In this lesson we will present some of the most common ways data is represented graphically.  W e will also discuss some of the ways you can increase the accuracy and effectiveness of graphs of data that you create.

Presenting Categorical Data Graphically

Visualizing data.

Categorical, or qualitative, data are pieces of information that allow us to classify the objects under investigation into various categories. We usually begin working with categorical data by summarizing the data into a frequency table.

Frequency Table

A frequency table is a table with two columns. One column lists the categories, and another for the frequencies with which the items in the categories occur (how many items fit into each category).

An insurance company determines vehicle insurance premiums based on known risk factors. If a person is considered a higher risk, their premiums will be higher. One potential factor is the color of your car. The insurance company believes that people with some color cars are more likely to get in accidents. To research this, they examine police reports for recent total-loss collisions. The data is summarized in the frequency table below.

Sometimes we need an even more intuitive way of displaying data. This is where charts and graphs come in.  There are many, many ways of displaying data graphically, but we will concentrate on one very useful type of graph called a bar graph.  In this section we will work with bar graphs that display categorical data; the next section will be devoted to bar graphs that display quantitative data.

A bar graph is a graph that displays a bar for each category with the length of each bar indicating the frequency of that category.

To construct a bar graph, we need to draw a vertical axis and a horizontal axis.  The vertical direction will have a scale and measure the frequency of each category; the horizontal axis has no scale in this instance.  The construction of a bar chart is most easily described by use of an example.

Using our car data from above, note the highest frequency is 52, so our vertical axis needs to go from 0 to 52, but we might as well use 0 to 55, so that we can put a hash mark every 5 units:

Notice that the height of each bar is determined by the frequency of the corresponding color.  The horizontal gridlines are a nice touch, but not necessary.  In practice, you will find it useful to draw bar graphs using graph paper, so the gridlines will already be in place, or using technology.  Instead of gridlines, we might also list the frequencies at the top of each bar, like this:

The following video explains the process and value of moving data from a table to a bar graph.

In this case, our chart might benefit from being reordered from largest to smallest frequency values. This arrangement can make it easier to compare similar values in the chart, even without gridlines. When we arrange the categories in decreasing frequency order like this, it is called a Pareto chart .

Pareto chart

A Pareto chart is a bar graph ordered from highest to lowest frequency

Transforming our bar graph from earlier into a Pareto chart, we get:

The following video addressed Pareto charts.

In a survey [1] , adults were asked whether they personally worried about a variety of environmental concerns. The numbers (out of 1012 surveyed) who indicated that they worried “a great deal” about some selected concerns are summarized below.

This data could be shown graphically in a bar graph:

To show relative sizes, it is common to use a pie chart.

A pie chart is a circle with wedges cut of varying sizes marked out like slices of pie or pizza.  The relative sizes of the wedges correspond to the relative frequencies of the categories.

For our vehicle color data, a pie chart might look like this:

Pie charts can often benefit from including frequencies or relative frequencies (percents) in the chart next to the pie slices. Often having the category names next to the pie slices also makes the chart clearer.

This video demonstrates how to create pie charts like the ones above.

The pie chart below shows the percentage of voters supporting each candidate running for a local senate seat.

If there are 20,000 voters in the district, the pie chart shows that about 11% of those, about 2,200 voters, support Reeves.

The following video addresses how to read a pie chart like the one above.

Pie charts look nice, but are harder to draw by hand than bar charts since to draw them accurately we would need to compute the angle each wedge cuts out of the circle, then measure the angle with a protractor. Computers are much better suited to drawing pie charts. Common software programs like Microsoft Word or Excel, OpenOffice.org Write or Calc, or Google Drive are able to create bar graphs, pie charts, and other graph types. There are also numerous online tools that can create graphs. [2]

Create a bar graph and a pie chart to illustrate the grades on a history exam below.

A: 12 students, B: 19 students, C: 14 students, D: 4 students, F: 5 students

Here is another way that fanciness can lead to trouble. Instead of plain bars, it is tempting to substitute meaningful images. This type of graph is called a pictogram .

A pictogram is a statistical graphic in which the size of the picture is intended to represent the frequencies or size of the values being represented.

Looking at the picture, it would be reasonable to guess that the manager salaries is 4 times as large as the worker salaries – the area of the bag looks about 4 times as large. However, the manager salaries are in fact only twice as large as worker salaries, which were reflected in the picture by making the manager bag twice as tall.

This video reviews the two examples of ineffective data representation in more detail.

Another distortion in bar charts results from setting the baseline to a value other than zero. The baseline is the bottom of the vertical axis, representing the least number of cases that could have occurred in a category. Normally, this number should be zero.

Compare the two graphs below showing support for same-sex marriage rights from a poll taken in December 2008 [3] . The difference in the vertical scale on the first graph suggests a different story than the true differences in percentages; the second graph makes it look like twice as many people oppose marriage rights as support it.

Presenting Quantitative Data Graphically

Visualizing numbers.

Quantitative, or numerical, data can also be summarized into frequency tables.

A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are:

19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0

These scores could be summarized into a frequency table by grouping like values:

Using the table from the first example, it would be possible to create a standard bar chart from this summary, like we did for categorical data:

A histogram is like a bar graph, but where the horizontal axis is a number line.

For the values above, a histogram would look like:

Notice that in the histogram, a bar represents values on the horizontal axis from that on the left hand-side of the bar up to, but not including, the value on the right hand side of the bar. Some people choose to have bars start at ½ values to avoid this ambiguity.

This video demonstrates the creation of the histogram from this data.

Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.

If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals .

Class Intervals

Class intervals are groupings of the data. In general, we define class intervals so that

• each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
• we have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.

Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Often time we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.

A histogram of this data would look like:

In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.

The following video walks through this example in more detail.

Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.

To see more about why a pie chart isn’t useful in this case, watch the following.

The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.

$140    $160    $160    $165    $180    $220    $235    $240    $250    $260    $280    $285

$285    $285    $290    $300    $300    $305    $310    $310    $315    $315    $320    $320

$330    $340    $345    $350    $355    $360    $360    $380    $395    $420    $460    $460

When collecting data to compare two groups, it is desirable to create a graph that compares quantities.

The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.

One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.

Frequency polygon

An alternative representation is a frequency polygon . A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.

This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.

The following video explains frequency polygon creation for this example.

• Gallup Poll. March 5-8, 2009. http://www.pollingreport.com/enviro.htm ↵
• For example: http://nces.ed.gov/nceskids/createAgraph/ or http://docs.google.com ↵
• CNN/Opinion Research Corporation Poll. Dec 19-21, 2008, from http://www.pollingreport.com/civil.htm ↵
• Learning Objectives and Introduction. Provided by : Lumen Learning. License : CC BY: Attribution
• Revision and Adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
• Math in Society. Authored by : David Lippman. Located at : http://www.opentextbookstore.com/mathinsociety/ . License : CC BY-SA: Attribution-ShareAlike
• Bar graphs for categorical data. Authored by : OCLPhase2's channel. Located at : https://youtu.be/vwxKf_O3ui0 . License : CC BY: Attribution
• Pareto Chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/Tsvru8DPxBE . License : CC BY: Attribution
• Creating a pie chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/__1f8dKh6yo . License : CC BY: Attribution
• Reading a pie chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/mwa8vQnGr3I . License : CC BY: Attribution
• Bad graphical representations of data. Authored by : OCLPhase2's channel. Located at : https://youtu.be/bFwTZNGNLKs . License : CC BY: Attribution
• numbers-education-kindergarten. Authored by : karanja. Located at : https://pixabay.com/en/numbers-education-kindergarten-738068/ . License : CC0: No Rights Reserved
• Creating a histogram. Authored by : OCLPhase2's channel. Located at : https://youtu.be/180FgZ_cTrE . License : CC BY: Attribution
• Defining class intervals for a frequency table or histogram. Authored by : OCLPhase2's channel. Located at : https://youtu.be/JhshitTtdP0 . License : CC BY: Attribution
• When not use a pie chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/FQ8zmZ56-XA . License : CC BY: Attribution
• Frequency polygons. Authored by : OCLPhase2's channel. Located at : https://youtu.be/rxByzA9MFFY . License : CC BY: Attribution

• Math Article
• Pictorial Representation Of Data

Pictorial Representation Of Data - Bar Graphs

Pictorial representation of data is called pictograph. As humanity flourished and the population increased, so did the amount of trade and transaction in the world. Ultimately, the amount of data is also increased. The merchants found it harder to keep track of the money flowing in and out of their coffers. When the population was little, trade was fairly simple but keeping track of who owes whom how much (data), so on and so forth became extremely tedious. To this end, the merchants created a bar graph with which they were able to depict a wide variety of information pictorially which not only helped understanding but also made it easier from a merchant’s point of view. What is the Bar Graph? Let’s find out.

Pictorial Representation Using Bar Graph

A bar graph also known as a bar chart is a chart that presents data that is grouped into rectangular bars. Here the length of the bar is directly proportional to the values they represent. The bar graph can be drawn vertically or horizontally.  A vertical bar graph is known as a Column Bar Graph . Since one bar graph can be used to display multiple groups of data on the same graph, bar graphs can also be used as comparative tools where the length of the rectangular bar represents the value of each category. Since the rectangular bars are proportional, their differences can be spotted much more easily, visually than through words. Let’s take a closer look at bar graphs.

Say you have pocket money of 100 rupees every week. You are allowed to spend this amount any which way you want to. You use this money to buy chocolate, beverages, food and other miscellaneous toys and stuff. What you notice is that every week, the money just seems to disappear. You ask your father for a little more money but he instead suggests that you see where the money is going so that you can learn the value of money. To this end, you grudgingly make a bar chart. But to create a bar chart, you need to have data. You need to note down the things you are spending money on and how much. After a week you have the details of this week’s expenditure and they look something like this

The first thing to observe is how the data is grouped. It is the first step to creating a bar graph. Similar expenses such as chocolates, candies, chewing gums are all grouped together. The same applies to the variety of soft drinks you consume. While discussing a bar graph, it was mentioned that the values are represented as a rectangular bar where the length of the rectangular bar is proportional to the value of the data. Here is where another characteristic of a bar graph comes into play.

A Bar Graph needs to have a uniform scale. The scale dictates the conversion of the data in number into the rectangular format. A bar graph is the representation of numbers using bars of uniform width and length dependent on the number.

For example, if you represent the money you spent on chocolate using a 25 cm long rectangular bar then the scale is 1 rupee is equal to one unit on the graph i.e. one rupee is represented by one centimeter. But you can clearly see that for this type of representation you will need a massive graph. The thing about scale is that it is completely under our control. So instead of 25 cm, you can represent the same quantity with a rectangular bar of length 25 millimeters and here the scale is 10 rupees is equal to the same one unit i.e. 10 rupees is represented by the same one centimeter.

The interpretation of data is heavily reliant on accurate information about the scale, therefore, it is extremely important to mention the scale of your graph along both the x-axis and y-axis. Using the latter scale i.e. 10 rupees is equal to one centimeter. It is important to remember that the same scale is applied to all the groups of data in the bar graph.

Properties of Bar Graph

• The width of each bar or column in a bar graph must be equal
• The base of the bars is common in a bar graph
• The height of bars represent the data in the bar graph, proportionally
• The bars can be drawn horizontally or vertically based on the given data

Types of Bar Graphs

In pictorial representation of data, the data is represented using a bar graph. There are three types of bar graphs that can be used for pictorial representation.

• Vertical bar graph
• Horizontal bar graph
• Double bar graph

Pictorial Representation of Data using Vertical Bar Graph

Vertical bar graphs are commonly used pictorial representations to express the given data using vertical bars. Here, the horizontal axis represents the categories and the vertical bars represent the corresponding data for each category. The horizontal axis is the x-axis and the vertical axis is the y-axis.

The vertical bar graphs are also used to represent the series of data and its variation over a period of time. All the vertical bars goes from the bottom of the x-axis to the top.

Pictorial Representation of Data Using Horizontal Bar graph

The horizontal bar graph represents the data using the bars that are parallel to the x-axis. The categories are defined along the y-axis and the respective data are represented using horizontal bars. The bars in the horizontal graph go from left to side along the x-axis.

Pictorial Representation of Data Using Double Bar Graph

You have seen what the bar graph of your expenses for the first week looks like. Say you continue this habit of tracking where you spent the money for some more time. You find that your week two expenses are slightly different from your first week. The details of the second-week expenses are;

Since they all belong to the same group, they can be charted on the same bar graph. Remember that the same scale applies to all the data in the graph. Instead of charting them individually, you can place similar groups next to each other to compare the changes over a larger time span or over a larger range of data. Now plotting this together, we are better poised to see the differences between the weekly expenditure.

This process can also help you control your expenditure because you now know what you are spending the most on. Through this, you can judge whether your expenses are necessary.

Related Articles

• Pictograph and Interpretation of a Pictograph
• Box and Whisker Plot

Frequently Asked Questions on Pictorial representation of data

What do you mean by pictograph, what are the different ways of pictorial representation of data, is a chart also a pictorial representation of data.

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