diagrammatic presentation of data bar diagrams and pie diagrams notes

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Diagrammatic Presentation Of Data

Introduction.

The diagrammatic representation also helps in having a bird’s eye view or overall view of the differentiation of data. It is a norm to present statistical data in the form of diagrams so that it becomes easier to comprehend and understand them. Therefore, diagrammatic representation is an important tool in statistics.

What is a Diagrammatic Presentation of Data?

Diagrammatic representation refers to a representation of statistical data in the form of diagrams. The diagrams used in representing statistical data are geometrical figures, such as lines, bars, and circles. The intention of using geometrical figures in statistical presentation is to make the study more interesting and easy to understand. Diagrammatic representations are widely used in statistics, economics, and many other fields of study.

Types of Diagrammatic Presentations of Data

Various types of diagrammatic representations of data depend on the dataset and the particular statistical elements in them. Data presentation can be made in different types and forms.

These can be broadly classified into the following one-dimensional types −

Line Diagram

In a line diagram, straight lines are used to indicate various parameters. Here, a line represents the sequence of data associated with the changing of a particular variable.

Properties of Line Diagram −

The Lines are either in vertical or horizontal directions.

There may be uniform scaling but this is not mandatory.

The lines that connect the data points offer the statistical representation of data.

The following is an example of a line diagram that shows profits in Rs crore from 2002 till 2008. Profit in 2002 was Rs 5 Crore while in 2008 it was Rs 24 Crore.

Bar Diagram

Bar diagrams have rectangular shapes of equal width that represent statistical data in a straightforward manner. Bar diagrams are one of the most widely used diagrammatic representations.

Properties of Bar Diagram −

The Bars can be vertical or horizontal in directions.

All bars in a diagram have a uniform width.

All the Bars have a common and same base.

The height or width of the Bar shows the required value.

The following is an example of a Bar Chart that has time on the X axis and profits on the Y axis.

Also known as a "circle chart" , the pie chart divides the circular statistical graphic into sectors or sections to illustrate the numerical data. Each sector in the circle denotes a proportionate part of the whole. Pie-chart works the best at the time when we want to denote the composition of something. In most cases, the pie chart replaces other diagrammatic representations, such as the bar graph, line plots, histograms, etc.

In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

Advantages of Diagrammatic Presentation of Data

Easier to understand.

Pictorial representations are usually easier to understand than statistical text or representation in tabular form. One can easily understand which portion or part has more contribution toward the overall dataset. This helps in understanding the data better.

The creators of diagrams usually keep the simplicity of presentation in mind to offer more information to readers. That is why diagrams are easier to comprehend than texts and tables.

More attractive

Pictorial or diagrammatic representations of datasets are more attractive than normal representations. As colors and various other tools can be incorporated into diagrams, they become more attractive and comprehensible for the readers.

Moreover, as diagrams can be made more interactive with the help of computer graphics, they have become more acceptable and attractive currently.

Simpler presentations

Data can be presented more simply in diagrammatic form. Both extensive unstable data and smaller complex data can be represented by diagrammatic representations more easily. This helps statisticians offer more value to their findings.

Comparison is easier

When two or more data are compared, it is easier to do so in pictorial form. As diagrams clearly show the portion of data consumed, it can be easily understood from the diagrams which part of the data is consuming more area in the diagrams. This can help one to understand the real differences through pictorial comparison.

Universal acceptance

Diagrammatic representation of data is used in many fields of study, such as statistics, science, commerce, economics, etc. So, the diagrams are accepted universally and hence are used everywhere.

Moreover, since there are the same procedures for forming diagrams, the representations mean the same thing to everyone. So, there is nothing to alter when we obtain the diagrams to check the real values. It helps analysts solve problems universally.

Improvement in presentation

Diagrammatic representations improve the overall representation of data to a large extent. As the data is classified into several groups and presented in a systematic manner in diagrams, the whole presentation of data gets improved during the diagrammatic representation.

Moreover, as diagrams can be made more interactive than texts or tables, diagrammatic presentations are one step ahead in presenting the data in a simpler yet recognizable manner.

More organized and classified data

To represent data in diagrams, they must be organized and classified into comprehensive categories. This helps the data to be organized in a given fashion which makes them orderly and creates a sequence. This in turn helps realize diagrammatic data better than text forms.

Relevance Diagrammatic Presentation of Data

Diagrams are a great way of representing data because they are visually attractive and they can make large, complex datasets look simpler. The otherwise heavy data can be simply and easily represented by line and bar diagrams, and pie charts. This makes data organization simpler and neater.

Moreover, as data must be classified before representation, one must organize them according to the norms required. So, diagrammatic representations save lots of time and resources.

Diagrams also have universal acceptance and so can be used to express data in different forms. This provides the analysts and researchers flexibility to present data in any required form.

Diagrams also remove confusion and offer a simpler tactic to present data. As no special skill has to be learned to represent data in diagrams, they can be used by most to show statistical data and results of various types of research and experiments.

Therefore, diagrammatic representation has great relevance that can be used for the benefit of economists, statisticians, marketing analysts, and a lot of other professionals.

The diagrams are a central part of statistics and their importance can be known from the fact that almost all statistical researchers use them in one way or the other. The diagrammatical representations make inferring statistical data much simpler and easier. It is a much easier way to visualize and understand data in simpler forms too.

To represent data in diagrammatic form, only a simple understanding of Mathematics is required. So, no special skills are needed to use diagrams and this makes them very popular tools for the representation of data sets. Learning how to present data in diagrams, therefore, should be a priority for everyone.

Q1. Which is the simplest diagrammatic presentation of data?

Ans. The simplest diagrammatic presentation of data is a line diagram that shows data in terms of straight lines.

Q2. What are the two characteristics of bar diagrams?

Ans. Bar diagrams have uniform width and their base remains the same.

Q3. How are the sections in a pie chart formed?

Ans. In practice, the various sections in a pie chart are derived according to their ratio to the total area of the circle. Then according to their individual contributions, sections are divided into parts derived from 360 degrees of the circle.

For example, if a section requires 25% of the presentation, it will consume  degrees on the chart.

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Statistics for Economics Class 11 Notes Chapter 4 Presentation of Data

July 5, 2019 by Sastry CBSE

Textual Presentation In textual presentation, data are a part of the text of study or a part of the description of the subject matter of study.

Tabular Presentation of Data “Tabulation involves the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration”

Components of a Table Following are the principal components of a table

• Table number
• Body or field

Classification of Data and Tabular Presentation (i) Qualitative Classification of Data and Tabular Presentation Qualitative classification occurs when data are classified on the basis of qualitative attributes or qualitative.

(ii) Characteristics of a Phenomenon

• Quantitative Classification of Data These occurs when data are classified on the basis ot quantitative characteristics of a phenomenon.
• Temporal Classified of Data In this, data are classified according to time, and time becomes the classifying variable.

(iii) Spatial Classification In spatial classification place, location becomes the classifying variable. It may be a village, a town, a district, etc. (iv) Merits of Tabular Presentation

• Simple and brief presentation
• Facilitates comparison
• Easy analysis
• High lights characteristics of data

Diagrammatic Presentation of Data These translates quite effectively the highly abstract ideas contained in numbers into more concrete and easily comprehensible form. Diagrammatic presentation is classified as given below (i) Bar Diagrams Bar diagrams are these diagrams in which data are presented in the form of bars or rectangles. Types of Bar Diagram are as follows

• Simple Bar Diagrams Simple bar diagrams are those diagrams which are based on a single set of numerical data.
• Multiple Bar Diagrams These are those diagram which show two or more sets of data simultaneously.
• Sub Divided Bar Diagram Sub-divided bar diagram are those diagrams which simultaneously present total values as well as part values of a set of data.
• Percentage Bar Diagram Percentage bar diagrams are those diagrams which show simultaneously, different parts of the values of a set of data in terms of percentages.

(ii) Pie or Circular Diagrams Pie diagram is a circle divided into various segments showing the per cent values of a series. This diagram does not show absolute values. (iii) Frequency Diagram Data in the form of grouped frequency distributions are generally represented by frequency diagram like histogram, frequency polygon, frequency curve and ogive.

• Histogram of equal class intervals
• Histogram of unequal class intervals
• Polygon Polygon is another form of diagrammatic presentation of data. It is formed by joining mid points of the tops of all rectangles in a histogram. However, a polygon can be drawn even without constructing a histogram.
• Frequency Curve A frequency curve is a curve which is plotted by joining the mid points of all tops of histogram by free hand smoothed curves and not by straight lines.
• Less than Method In this method, beginning from upper limit of the 1st values we go on adding the frequencies corresponding to every next upper limit of the series.
• More than Method In this method, we take cumulative total of the frequencies beginning with lower limit of the 1st class interval.

(iv) Arithmetic Line Graph An arithmetic line graph is also called time series graph. In it time is plotted along x-axis and the value of the variable along y-axis. A line graph by joining these plotted points, these obtained is called time series graph.

Rules for Constructing a Graph

• Choice of scale
• Proportion of axis
• Method of plotting the points
• Lines of different types
• Table of data
• Use of false line
• One Variable Graph One variable graph are those graphs in which values of only one variable are shown with respect to some time period.
• Two or More than Two Variable Graphs These – are the graphs in which values of two variables are simultaneously shown with respect to some period of time.

Merits of Diagrammatic and Graphic Presentation

• Simple and understandable information
• Lasting impact
• No need of training or specialised knowledge
• Attractive and effective means of presentation
• A quick comparative glance
• Information and entertaining
• Location of averages
• Study of correlation

Limitations of Diagrammatic and Graphic Presentation

• Limited use
• Only preliminary conclusions

Statistics for Economics Class 11 Notes

Class 11 economics notes, free resources.

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• Class 11 Commerce
• T.R. Jain and V.K. Ohri Solutions
• Chapter 6 Diagrammatic Presentation Of Data Bar Diagrams And Pies Diagrams

T.R. Jain and V.K. Ohri Solutions Class 11 Statistics Economics Chapter 6 - Diagrammatic Presentation of Data- Bar Diagrams and Pies Diagrams

T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 6 – Diagrammatic Presentation of Data: Bar diagrams and Pie diagrams is regarded as an important concept to be studied thoroughly by the students. Here, we have provided T.R. Jain and V.K. Ohri Solutions for Class 11 .

Chapter 6: Diagrammatic Presentation of Data : Bar Diagrams and Pie Diagrams cover the below-mentioned concepts.

•       What is a bar diagram?
•       Types of bar diagram
•       Pie or Circular diagrams
•       Multiple bar diagram

T.R. Jain and V.K. Ohri Solutions for Class 11 Statistics for Economics Chapter 6 – Diagrammatic Presentation of Data- Bar Diagrams and Pies Diagrams

Represent the following data by a percentage bar diagram.

Draw a suitable diagram to represent the following information.

Also, show profit and loss.

First of all, we shall calculate the cost (wages, materials, miscellaneous) and profit per unit as given in the following table.

Note:  (Negative profit is regarded as a loss.)

An appropriate diagram for representing this data would be the rectangle whose widths are in the ratio of the quantities sold, i.e, 20:30, i.e, 2:3. Selling prices would be represented by the corresponding heights of the rectangles with various costs (wages, materials, miscellaneous), and the profit or loss represented by the various divisions of the rectangles as shown in the diagram given on the next page.

(Note: In case of profit, i.e., when selling price > cost price, the entire rectangle will lie above the X-axis. However, in case of loss, we will have a rectangle with a portion lying below the X-axis which will reflect the loss incurred and it cannot be recovered through sales.)

Following are the data about the market share of four brands of TV sets sold in Panipat and Ambala. Present the data in the pie chart.

Total sets sold in Place A and Place B are 1,200 and 1,875 respectively. Data are to be represented by two circles whose radii are in the ratio of square roots of total TV sets sold in each city in the ratio of 1:1. The calculations regarding the construction of the pie diagram are as follows.

The following table shows the interest of students in a school in different games.

The following table shows the monthly expenditure of different families on different items.

Represent the data in the form of a sub-divided bar diagram.

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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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45 Presentation of data I – Diagrammatic representation

Pa . Raajeswari

INTRODUCTION

The data we collect can often be more easily understood for interpretation if it is presented graphically or pictorially. Diagrams and graphs give visual indication of magnitudes, grouping, trends and patterns in the data. The diagrams are used for facilitating comparisons between two or more sets of data. The diagrams are more suitable to illustrate the discrete data. The diagrams should be clear and easy to read and understand.

A large number of diagrams are used to present statistical data. The choice of a particular diagram to present a given set of numerical data is not an easy one. It primarily depends on the nature of the data, magnitude of the observations and the type of people for whom the diagrams are meant and requires great amount of expertise, skill and intelligence. An inappropriate choice of the diagram for the given set of data might give a distorted picture of the phenomenon under the study and might lead to wrong and fallacious interpretations and conclusions. Hence, the choice of a diagram to present the given data should be made with utmost caution and care. The diagrams do not add any meaning to the statistical facts, but they exhibit the results more clearly. Use of diagrams is becoming more and morepopular in the present scenario.

REPRESENTATION OF DATA

Besides the tabular form, the data may also be presented in some graphic or diagrammatic form. “The transformation of data through visual methods like graphs, diagrams, maps and charts is called representation of data.”

The need of representing data graphically:

Graphics, such as maps, graphs and diagrams, are used to represent large volume of data. They are necessary:

• If the information is presented in tabular form or in a descriptive  record, it becomes difficult to draw results.
• Diagramatic form makes it possible to easily draw visual impressions of data.
• The diagramatic method of the representation of data enhances our understanding.
• It makes the comparisons easy.
• Besides, such methods create an imprint on mind for a longer time.
• Diagrams are visual aids for presentation of statistical data and more appealing.
• It is a time consuming task to draw inferences about whatever is being presented in non–diagramaticform.
• It presents characteristics in a simplified way.
• These makes it easy to understand the patterns of population growth, distribution and the density, sex ratio, age–sex composition, occupational structure, etc.

General Rules for Drawing Diagrams and Maps

1. Selection of a Suitable Diagrammatic Method

Each characteristic of the data can only be suitably represented by an appropriate diagramatic method. For example,

To show the data related to the temperature or growth of population between different periods in time line graph are used.

Similarly, bar diagrams are used for showing rainfall or the production of commodities.

The population distribution, both human and livestock, or the distribution of the crop producing areas are shown by dot maps.

The population density can be shown by choropleth maps.

Thus, it is necessary and important to select suitable diagramatic method to represent data.

2. Selection of Suitable Scale

Each diagram or map is drawn to a scale which is used to measure the data. The scale must cover the entire data that is to be represented. The scale should neither be too large nor too small.

The diagram or map should have following design:

1.  Title: The title of the diagram/map must be clear and include – o The name of the area,  Reference year of the data used and o The caption of the diagram.

These are written with different font sizes and thickness. The title, subtitle and the corresponding year is shown in the centre at the top of the map/diagram.

2.   Legend or Index : The index must clearly explain the colours, shades, symbols and signs used in the map and diagram. A legend is shown either at the lower left or lower right side of the map sheet.

3.  Direction The maps should show the direction North and properly placed on the top.

Types of Diagrams

A research should contain a large variety of diagrammatic presentations to present the data and findings of research work.

• One dimensional diagrams – Line and Bar diagram.
• Two dimensional diagrams – Pie diagram
• Three dimensional diagram – Cubes,Squares,Prisms, Cylinders and Blocks.
• Pictographs

ONE DIMENSIONAL DIAGRAMS

1.    LINE DIAGRAM

This kind of a diagram becomes suitable for representing data supplied chronologically in an ascending or descending order. It shows the behaviour of a variable over time. The line graphs are usually drawn to represent the time series data related to the temperature, rainfall, population growth, birth rates and the death rates.

Construction of a Line Graph

1st step: Round the data to be shown upto 1 digit of even numbers.

2nd step: Draw X and Y-axis. Mark the time series variables (years/months) on the X axis and the data quantity/value to be plotted on Y axis.

3rd step: Choose an appropriate scale to show data and label it on Y-axis. If the data involves a negative figure then the selected scale should also show it.

4th step: Plot the data to depict year/month-wise values according to the selected scale on Y-axis, mark the location of the plotted values by a dot and join these dots by a free hand drawn line

Construct a line graph to represent the data

Line diagrams are the simplest of all diagrams.

Line graph is most useful in displaying data or information that change continuously over time.

2. Polygraph

Polygraph is a line graph in which two or more than two variables are shown on a same diagram by different lines. It helps in comparing the data. Examples which can be shown as polygraph are:

• The growth rate of different crops like rice, wheat, pulses in one diagram.
• The birth rates, death rates and life expectancy in one diagram.
• Sex ratio in different states or countries in one diagram.

Construction of a Polygraph

All steps of construction of polygraph are similar to that of line graph. But different lines are drawn to indicate different variables.

Construct a polygraph to compare the variables.

3. Bar Diagram

It is also called a columnar diagram. The bar diagrams are drawn through columns of equal width. Following rules were observed while constructing a bar diagram:

(a)  The width of all the bars or columns is similar.

(b)  All the bars should are placed on equal intervals/distance.

(c)  Bars are shaded with colours or patterns to make them distinct and attractive.

Three types of bar diagrams are used to represent different data sets:

• The simple bar diagram
• Compound bar diagram
• Polybar diagram.

Simple Bar Diagram

Construction  of   a simple  bar diagram

A simple bar diagram is constructed for an immediate comparison. It is advisable to arrange the given data set in an ascending or descending order and plot the data variables accordingly. However, time series data are represented according to the sequencing of the time period.

Construction Steps:

Draw X and Y- axes on a graph paper. Take an interval and mark it on Y-axis to plot data. Divide X-axis into equal parts to draw bars. The actual values will be plotted according to the selected scale.

Line and Bar Graph

The line and bar graphs as drawn separately and may also be combined to depict the data related to some of the closely associated characteristics such as the climatic data of mean monthly temperatures and rainfall.

                                        Construct a Line and bar Graph

Construction:

• Draw X and Y-axes of a suitable length and divide X-axis into parts to show months in a year.
• Select a suitable scale with equal intervals on the Y-axis and label it at its right side.
• Similarly, select a suitable scale with equal intervals on the Y-axis and label at its left side.
• Plot data using line graph and columnar diagram.

Multiple Bar Diagram

Multiple bar diagrams are constructed to represent two or more than two variables for the purpose of comparison. For example, a multiple bar diagram may be constructed to show proportion of males and females in the total, rural and urban population or the share of canal, tube well and well irrigation in the total irrigated area in different states.

              Construct a Multiple bar Diagram.

Construction

(a) Mark time series data on X-axis and variable data on Y-axis as per the selected scale.

(b) Plot the data in closed columns.

• Compound Bar Diagram

When different components are grouped in one set of variable or different variables of one component are put together, their representation is made by a compound bar diagram. In this method, different variables are shown in a single bar with different rectangles.

Construct a Compound Bar Diagram

• Arrange the data in ascending or descending order.
• A single bar will depict the set of variables by dividing the total length of the bar as per percentage.

TWO DIMENSIONAL DIAGRAMS

• Pie Diagram

Pie diagram is another diagramatic method of the representation of data. It is drawn to depict the total value of the given attribute using a circle. Dividing the circle into corresponding degrees of angle then represent the sub– sets of the data. Hence, it is also called as Divided Circle Diagram. The angle of each variable is calculated using the following formulae.

Pie Diagram.

If data is given in percentage form, the angles are calculated using the given formulae.

Calculation of Angles:

(a) Arrange the data on percentages in an ascending order.

(b) Calculate the degrees of angles for showing the given values

(b)It could be done by multiplying percentage with a constant of 3.6 as derived by dividing the total number of degrees in a circle by 100,

                        i.  e. 360/100.

(c)Plot the data by dividing the circle into the required number of divisions to show the share different regions/countries

(a)Select a suitable radius for the circle to be drawn. A radius of 3, 4 or 5 cm may be chosen for the given data set.

(b)Draw a line from the centre of the circle to the arc as a radius.

(c)Measure the angles from the arc of the circle for each category of vehicles in an ascending order clock-wise, starting with smaller angle.

(d) Complete the diagram by adding the title, sub – title, and the legend. The legend mark be chosen for each variable/category and highlighted by distinct shades/colours.

Precautions

(a)The circle should neither be too big to fit in the space nor too small to be illegible.

(b) Starting with bigger angle will lead to accumulation of error leading to the plot of the smaller angle difficult.

THREE DIMENSIONAL DIAGRAMS

These diagrams are used when only one point is to be compared and the ratio between the highest and the lowest measurements is more than 100. For these diagrams, the cube root of various measurements is calculated and the side of each cube istaken in proportion to the cube roots

Among the three dimensional diagrams, cubes are the easiest and should be used only in cases where the figures cannot be adequately presented through bar, square or circle diagrams.In case of cubes, all three dimensions, length, width and height are taken into consideration.In case of a cylinder, the length and diameter of circle are taken into consideration. A sphere in the shape of a bell can be used in a three dimensional form.

Pictograph is a way of representing statistical data using symbolic figures to match the frequencies of different kinds of data.A pictogram is another form of pictoral bar chart. Such charts are useful in presenting data to people whocannot understand charts.Small symbols or simple figures are used to represent the size of data.

To construct pictograms, the following suggestions are made;

• The symbols must be simple and clear.
• The quantity represented by the symbol should be given
• Large quantities are shown by increasing the number and not by increasing the size of symbols. A part of symbol can be used to represent a quantity smaller than the whole symbol

Major advantages of pictograms

• First, they are farmore attractive when compared to other diagrams. As such they generate interest in audience.
• Second, it has been observed that the facts presentedby pictograms are remembered for long time than tables, bars and other diagrams.

Limitations of pictograms

• First, they are difficult to draw
• we cannot show the actual data properly

Cartograms are the maps used to present the statistical data on a geographical basis. The various figures in different regions on maps are shown either by

• Shades or colours
• Dots or bars
• Diagrams or pictures
• By putting numerical figures in each geographical area.

CLASSIFIATION

There are three main types of cartograms, each have a very different way of showing attributes of geographic objects-

• Non-contiguous,
• Contiguous and
• Dorling cartograms.

NON-CONTIGUOUS CARTOGRAMS

A non-contiguous cartogram is the simplest and easiest type of cartogram to make. In a non-contiguous cartogram, the geographic objects do not have to maintain connectivity with their adjacent objects. This connectivity is called topology. By freeing the objects from their adjacent objects, they can grow or shrink in size and still maintain their shape. Here is an example of two non-contiguous cartograms.

The cartogram on the left has maintained the object’s centroid (a centroid is the weighted center point of an area object.) Because the object’s center is staying in the same place, some of the objects will begin to overlap when the objects grow or shrink depending on the attribute (in this case population.) In the cartogram on the right, the objects not only shrink or grow, but they also will move one way or another to avoid overlapping with another object.

CONTIGUOUS CARTOGRAMS

In a non-contiguous cartogram topology was sacrificed in order to preserve shape. In a contiguous cartogram, the reverse is true- topology is maintained (the objects remain connected with each other) but this causes great distortion in shape.The cartographer must make the objects the appropriate size to represent the attribute value, but he or she must also maintain the shape of objects as best as possible, so that the cartogram can be easily interpreted. Here is an example of a contiguous cartogram of population in California’s countries. Compare this to the previous non-contiguous cartogram.

DORLING CARTOGRAM

A Dorling cartogram maintains neither shape, topology nor object centroids, though it has proven to be a very effective cartogram method. To create a Dorling cartogram, instead of enlarging or shrinking the objects themselves, the cartographer will replace the objects with a uniform shape, usually a circle, of the appropriate size.

Secondly, the Dorling Cartogram attempts to move the figures the shortest distance away from their true locations

Another Dorling-like cartogram is the Demers Cartogram, which is different in two ways. It uses squares rather than circles; this leaves fewer gaps between the shapes. The Demers cartogram often sacrifices distance to maintain contiguity between figures, and it will also sacrifice distance to maintain certain visual cues (The gap between figures used to represent San Francisco Bay in the Demers Cartogram below is a good example of a visual cue)

PSEUDO-CARTOGRAMS

Pseudo-cartograms (or false cartograms ) are representations that may look like cartograms but do not follow certain cartogram rules. Perhaps the most famous type of pseudo-cartogram was developed by Dr. Waldo Tobler. In this case, instead of enlarging or shrinking the objects themselves, Tobler moves the object’s connections to a reference grid such as latitude or longitude in order to give the same effect. This maintains good directional accuracy in the cartogram (if county A is directly north of county B, it will still remain directly north in the cartogram .Note in previous examples, such as the Dorling Cartogram, this is not always true) however; this is a false cartogram because it creates extensive error in the actual size of the objects

ADVANTAGES OF CARTOGRAMS

• Cartograms are simple and easy to understand.
• They are generally used when the regional or geographical comparisons are to be made.

LIMITATIONS

• Cartograms are very attractive but they should be used especially where geographic comparisons are to be made and where approximate measures can serve the purpose.
• This is understandable as the maps are unable to provide 100% accuracy.

. No single diagram is suited for all practical situations. The choice of a particular diagram for visual presentation of a given set of data is not an easy one and requires great skill, intelligence and expertise. The choice will primarily depend upon the nature of the data and object of the presentation, i.e., the type of the audience to whom the diagrams are to be presented and it should be made with utmost care and caution. A wrong or  injudicious selection of the diagram will distort the true characteristics of the phenomenon to be presented and might lead to very wrong and misleading interpretations.

• https://gradestack.com/Class-11th-Commerce/Presentation-of-Data/Diagrammatic-Presentation/17643-3574-27365-study-wtw
• http://www.economicsdiscussion.net/statistics/data/graphical-representation-of-statistical-data/12010
• https://www.scribd.com/doc/41044016/Diagrammatic-Graphical-Presentation-of-Data
• http://www.publishyourarticles.net/knowledge-hub/statistics/diagrammatic-presentation-of-data/1103/
• https://www.youtube.com/watch?v=2TMs4-hIA04

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Diagrammatic Presentation of Data: Meaning , Features, Guidelines, Advantages and Disadvantages

Diagrammatic presentation of data.

The technique of presenting statistical data in the form of diagrams such as bar diagrams, cartograms, pie diagrams, and pictograms is known as the Diagrammatic Presentation of Data.

Statistics performs an important function by presenting a complex mass of data in a simple way that makes it easier to understand. Classification and tabulation are two techniques for presenting data in an understandable form. However, as the volume of data increases, it becomes increasingly inconvenient to understand, even after classification and tabulation. Thus, data is presented in the form of diagrams and graphs to enable the comparison of various situations and to understand the various patterns in the data at a glance.

Features of Diagrammatic Presentation of Data

• The diagrams have the unique ability to display statistical facts in the shape of attractive and appealing pictures and charts, without the need for figures altogether.
• One of the most convincing and appealing ways to present statistical results is using diagrammatic presentation.
• Diagrammatic data presentation transforms the highly abstract ideas contained in figures into a more concrete and easily understandable form.
• Evidence of this may be found in newspapers, magazines, advertisements, books, television, and so on.

The tabular data is difficult to understand for a layman. However, a single glance at the diagram provides a thorough picture of the presented data. Thus, the diagrammatic representation method is simple and easy to understand.

General Guidelines for Diagrammatic Presentation

The construction of diagrams is an art that may be learned through practice. While drawing diagrams, the following general rules/directions should be followed:

1. Appropriate Title: Each diagram should include a suitable title/heading that clearly shows the main idea or theme that the diagram wants to convey. The title/heading should be simple, clear, precise, and self-explanatory.

2. Size: The size of a diagram is determined by the quantity of data to be shown. The size should be such that it covers all of the important features of the data and can be understood by a simple glance at the diagram. The size of diagrams should be determined by the available space. It should be neither too big nor too small.

3. Proportion between Width and Height: An appropriate proportion of the diagram’s height (Vertical axis or Y-axis) and width (Horizontal axis or X-axis) should be made. If either (height or width) is too short or too long in proportion, the diagram would look bad.

4. Scale: The scale for the diagram should be selected so that the figures created may clearly represent the necessary details.

• The scale should be in even numbers or multiples of 10, 20, 30, and 40, as much as possible.
• Avoid using odd numbers such as 1, 3, 5, 7, 9, 11, and so on.
• The scale (for example, 1 cm = 10,000) should always be mentioned below the heading.

When the same set of data is displayed on multiple scales, the size of the diagrams may differ significantly, leading to incorrect and misleading interpretations. Therefore, it is essential to select the scale with great care and caution.

5. Index: When various things are presented on a single diagram, different shades and colours should be used to differentiate them. For easy identification and understanding of these different shades, an index describing them should also be provided.

6. Attractive Presentation: A diagram should be designed in such a way that it makes an immediate impact on the viewer. The diagram should be constructed properly and cleanly in order to attract the reader.

7. Accuracy: Diagrams should be drawn accurately by using appropriate measurement scales. Simply put. accuracy should not be compromised for appearance.

8. Simplicity: Diagrams should be as simple as possible so that the layman can easily understand their meaning.

9. Selection of a Proper Diagram: There are a number of geometrical techniques (diagrams) that can be used to show statistical data. Due to the fact that not all types of diagrams are appropriate for all types of data, extra care should be taken while selecting a particular diagram for presenting a set of figures.

Advantages of Diagrammatic Presentation

Diagrams, which provide a bird’s-eye view of a large amount of statistical data, are extremely useful and important. Following are some of the advantages of diagrammatic presentation:

1. Diagrams are Attractive and Impressive: The data presented in the form of diagrams may even grab the attention of a common person. It means that diagrams generate more interest than figures. In everyday life, one skip over the figures and instead focuses on the diagrams while reading journals, newspapers, magazines, and so on. Thus, diagrams are widely used in board meetings, conferences, exhibitions, seminars, and public functions.

2. Diagrams Facilitate Comparison: Using diagrams to illustrate two sets of data makes it easier to compare them. For example , with the help of diagrams, it becomes easy to compare the growth rate of the population of different countries.

3. Diagrams Simplify Data: Diagrams are used to represent a huge mass of complex data in a simplified and understandable format.

4. Universal Applicability: This technique can be applied universally at any time and is used in almost all subjects and other fields.

5.  Easy to Remember: Diagrams are extremely effective as they help in easily memorising information. The image generated in the mind by the diagrams lasts much longer compared to those created by figures presented in tabular form.

6. Diagrams Save Time: Diagrams present complex data in a simplified form. Hence, facts presented in the form of diagrams can be quickly understood. Besides, studying the trend and significance of voluminous data takes a long time.

7. Diagrams Provide More Information: Diagrams not only display the characteristics of data but also show hidden facts and relationships which are not possible from classified and tabulated data.

Disadvantages of Diagrammatic Presentation

Nowadays, diagrams are extremely popular. However, despite their usefulness, they have some limitations. Following are some of the limitations of diagrammatic presentation:

1. No Utility to Experts: Diagrams only provide a general understanding of the problem, which may be useful to the common person but not to experts who need an exact idea of the problem.

2. Limited Information: Diagrams only provide limited and approximate information. One must refer to the original statistical tables for more precise and in-depth information.

3. Minute Difference Presentation Is Impossible: Diagrams cannot show minute differences in large figures (observations). The precision of the values shown in the diagrams is extremely low. For instance, it will be difficult to tell the difference between two large values, such as 9,500 and 9,530, when represented in the form of a diagram.

4. Can easily be Misused: The use of the wrong type of diagram will result in an incorrect (deceptive) inference. Hence, one should always take measures to prevent them.

5. Lack of Further Analysis: Diagrams cannot be further studied for analysis.

6. Can only be used for Comparative Studies: Diagrams are only useful when comparisons are required. A single diagram is not much important. It can only be interpreted when compared to another diagram.

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Diagrammatic Presentation of Data- Bar Diagrams & Pies Class 11 Solutions TR Jain (PDF Available)

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