diagrammatic presentation of time series data is known as

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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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• 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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• Diagrammatic Presentation Of Data

Diagrammatic Presentation of Data

The diagrammatic presentation of data gives an immediate understanding of the real situation to be defined by the data in comparison to the tabular presentation of data or textual representations. It translates the highly complex ideas included in numbers into a more concrete and quickly understandable form pretty effectively. Diagrams may be less certain but are much more efficient than tables in displaying the data. There are many kinds of diagrams in general use. Amongst them the significant ones are the following:

(i) Geometric diagram

(ii) Frequency diagram

(iii) Arithmetic line graph

Also check: Meaning and Objective of Tabulation

Basics of Diagrammatic Presentation

Concept of Diagrammatic Presentation

• It is a technique of presenting numeric data through pictograms, cartograms, bar diagrams, and pie diagrams. It is the most attractive and appealing way to represent statistical data. Diagrams help in visual comparison and they have a bird’s eye view.
• Under pictograms, we use pictures to present data. For example, if we have to show the production of cars, we can draw cars. Suppose the production of cars is 40,000, we can show it by a picture having four cars, where 1 car represents 10,000 units.
• Under cartograms, we make use of maps to show the geographical allocation of certain things.
• Bar diagrams are rectangular and placed on the same base. Their heights represent the magnitude/value of the variable. The width of all the bars and the gaps between the two bars are kept the same.
• Pie diagram is a circle that is subdivided or partitioned to show the proportion of various components of the data.
• Out of the given diagrams, only one-dimensional bar diagrams and pie diagrams are there in our scope.

General Guidelines

Title: Every diagram must be given a suitable title which should be small and self-explanatory.

Size: The size of the diagram should be appropriate, i.e., neither too small nor too big.

Paper used: Diagrams are generally prepared on blank paper.

Scale: Under one-dimensional diagrams, especially bar diagrams, the y-axis is more important from the point of view of the decision of scale because we represent magnitude along this axis.

Index: When two or more variables are presented and different types of line/shading patterns are used to distinguish, an index must be given to show their details.

Selection of proper type of diagram: It is very important to select the correct type of diagram to represent data effectively.

Advantages of Diagrammatic Presentation

(1) Diagrams are attractive and impressive:   The data presented in the form of diagrams can attract the attention of even a common man.

(2) Easy to remember:    (a)  Diagrams have a great memorising effect. (b)  The picture created in mind by the diagrams last much longer than those created by figures presented through the tabular forms.

(3) Diagrams save time : (a)  They present complex mass data in a simplified manner. (b)  The data presented in the form of diagrams can be understood by the user very quickly.

(4) Diagrams simplify data:   Diagrams are used to represent a huge mass of complex data in a simplified and intelligible form which is easy to understand.

(5) Diagrams are useful in making comparison:   It becomes easier to compare two sets of data visually by presenting them through diagrams.

(6) More informative :   Diagrams not only depict the characteristics of data but also bring out other hidden facts and relations which are not possible from the classified and tabulated data.

Types of One-Dimensional Diagram

One-dimensional diagram is a diagram in which only the length of the diagram is considered. It can be drawn in the form of a line or various types of bars.

The following are the types of one-dimensional diagram.

(1) Simple bar diagram

Simple bar diagram consists of a group of rectangular bars of equal width for each class or category of data.

(2) Multiple bar diagram

This diagram is used when we have to make a comparison between two or more variables like income and expenditure, import and export for different years, marks obtained in different subjects in different classes, etc.

(3) Subdivided bar diagram

This diagram is constructed by subdividing the bars in the ratio of various components.

(4) Percentage bar diagram

The subdivided bar diagram presented on a percentage basis is known as the percentage bar diagram.

(5) Broken-scale bar diagram

This diagram is used when the value of one observation is very high as compared to the other.

To gain space for the smaller bars of the series, the larger bars may be broken.

The value of each bar is written at the top of the bar.

(6) Deviation bar diagram

Deviation bars are used to represent net changes in the data like net profit, net loss, net exports, net imports, etc.

Meaning of Pie Diagram

A pie diagram is a circle that is divided into sections. The size of each section indicates the magnitude of each component as a part of the whole.

Steps involved in constructing pie diagram

• Convert the given values into percentage form and multiply it with 3.6’ to get the amount of angle for each item.
• Draw a circle and start the diagram at the 12 O‘clock position.
• Take the highest angle first with the protector (D) and mark the lower angles successively.
• Shade different angles differently to show distinction in each item.

Solved Questions

Q.1. Why is a diagrammatic presentation better than tabulation of data?

It makes the data more attractive as compared to tabulation and helps in visual comparison.

Q.2. Why do media persons prefer diagrammatic presentation of data?

Because it has an eye-catching effect and a long-lasting impact upon its readers/viewers.

Q.3. What will be the degree of an angle in the pie diagram if a family spends 50% of its income in food?

(50 ÷ 100) X 360 (Or) 50 x 3.6 = 180’

Q.4. Which bar diagram is used to show two or more characteristics of the data?

Multiple bar diagram

Q.5. Mention the sum of all the angles formed at the centre of a circle.

Q.6. Name a bar diagram where the height of all the bars is the same.

Percentage bar diagram

Q.7. Which diagram can be used to depict various components of a variable?

Subdivided bar diagram

Q.8. What is a multiple bar diagram?

A multiple bar diagram is one that shows more than one characteristic of data.

Q.9. Which bar diagram is used to represent the net changes in data?

Deviation bar diagram

Q.10. What is the other name of the subdivided bar Diagram?

Component bar diagram

The above-mentioned concept is for CBSE Class 11 Statistics for Economics – Diagrammatic Presentation of Data. For solutions and study materials, visit our website or download the app for more information and the best learning experience.

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• Accountancy
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• CBSE Class 11 Statistics for Economics Notes

Chapter 1: Concept of Economics and Significance of Statistics in Economics

• Statistics for Economics | Functions, Importance, and Limitations

Chapter 2: Collection of Data

• Data Collection & Its Methods
• Sources of Data Collection | Primary and Secondary Sources
• Direct Personal Investigation: Meaning, Suitability, Merits, Demerits and Precautions
• Indirect Oral Investigation : Suitability, Merits, Demerits and Precautions
• Difference between Direct Personal Investigation and Indirect Oral Investigation
• Information from Local Source or Correspondents: Meaning, Suitability, Merits, and Demerits
• Questionnaires and Schedules Method of Data Collection
• Difference between Questionnaire and Schedule
• Qualities of a Good Questionnaire and types of Questions
• What are the Published Sources of Collecting Secondary Data?
• What Precautions should be taken before using Secondary Data?
• Two Important Sources of Secondary Data: Census of India and Reports & Publications of NSSO
• What is National Sample Survey Organisation (NSSO)?
• What is Census Method of Collecting Data?
• Sample Method of Collection of Data
• Methods of Sampling
• Father of Indian Census
• What makes a Sampling Data Reliable?
• Difference between Census Method and Sampling Method of Collecting Data
• What are Statistical Errors?

Chapter 3: Organisation of Data

• Organization of Data
• Objectives and Characteristics of Classification of Data
• Classification of Data in Statistics | Meaning and Basis of Classification of Data
• Concept of Variable and Raw Data
• Types of Statistical Series
• Difference between Frequency Array and Frequency Distribution
• Types of Frequency Distribution

Chapter 4: Presentation of Data: Textual and Tabular

• Textual Presentation of Data: Meaning, Suitability, and Drawbacks
• Tabular Presentation of Data: Meaning, Objectives, Features and Merits
• Different Types of Tables
• Classification and Tabulation of Data

Chapter 5: Diagrammatic Presentation of Data

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

Types of Diagrams

• Bar Graph | Meaning, Types, and Examples
• Pie Diagrams | Meaning, Example and Steps to Construct
• Histogram | Meaning, Example, Types and Steps to Draw
• Frequency Polygon | Meaning, Steps to Draw and Examples
• Ogive (Cumulative Frequency Curve) and its Types
• What is Arithmetic Line-Graph or Time-Series Graph?
• Diagrammatic and Graphic Presentation of Data

Chapter 6: Measures of Central Tendency: Arithmetic Mean

• Measures of Central Tendency in Statistics
• Arithmetic Mean: Meaning, Example, Types, Merits, and Demerits
• What is Simple Arithmetic Mean?
• Calculation of Mean in Individual Series | Formula of Mean
• Calculation of Mean in Discrete Series | Formula of Mean
• Calculation of Mean in Continuous Series | Formula of Mean
• Calculation of Arithmetic Mean in Special Cases
• Weighted Arithmetic Mean

Chapter 7: Measures of Central Tendency: Median and Mode

• Median(Measures of Central Tendency): Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Median for Different Types of Statistical Series
• Calculation of Median in Individual Series | Formula of Median
• Calculation of Median in Discrete Series | Formula of Median
• Calculation of Median in Continuous Series | Formula of Median
• Graphical determination of Median
• Mode: Meaning, Formula, Merits, Demerits, and Examples
• Calculation of Mode in Individual Series | Formula of Mode
• Calculation of Mode in Discrete Series | Formula of Mode
• Grouping Method of Calculating Mode in Discrete Series | Formula of Mode
• Calculation of Mode in Continuous Series | Formula of Mode
• Calculation of Mode in Special Cases
• Calculation of Mode by Graphical Method
• Mean, Median and Mode| Comparison, Relationship and Calculation

Chapter 8: Measures of Dispersion

• Measures of Dispersion | Meaning, Absolute and Relative Measures of Dispersion
• Range | Meaning, Coefficient of Range, Merits and Demerits, Calculation of Range
• Calculation of Range and Coefficient of Range
• Interquartile Range and Quartile Deviation
• Partition Value | Quartiles, Deciles and Percentiles
• Quartile Deviation and Coefficient of Quartile Deviation: Meaning, Formula, Calculation, and Examples
• Calculation of Mean Deviation for different types of Statistical Series
• Mean Deviation from Mean | Individual, Discrete, and Continuous Series
• Standard Deviation: Meaning, Coefficient of Standard Deviation, Merits, and Demerits
• Standard Deviation in Individual Series
• Methods of Calculating Standard Deviation in Discrete Series
• Methods of calculation of Standard Deviation in frequency distribution series
• Combined Standard Deviation: Meaning, Formula, and Example
• How to calculate Variance?
• Coefficient of Variation: Meaning, Formula and Examples
• Lorenz Curveb : Meaning, Construction, and Application

Chapter 9: Correlation

• Correlation: Meaning, Significance, Types and Degree of Correlation
• Methods of measurements of Correlation
• Calculation of Correlation with Scattered Diagram
• Spearman's Rank Correlation Coefficient
• Karl Pearson's Coefficient of Correlation
• Karl Pearson's Coefficient of Correlation | Methods and Examples

Chapter 10: Index Number

• Index Number | Meaning, Characteristics, Uses and Limitations
• Methods of Construction of Index Number
• Unweighted or Simple Index Numbers: Meaning and Methods
• Methods of calculating Weighted Index Numbers
• Fisher's Index Number as an Ideal Method
• Fisher's Method of calculating Weighted Index Number
• Paasche's Method of calculating Weighted Index Number
• Laspeyre's Method of calculating Weighted Index Number
• Laspeyre's, Paasche's, and Fisher's Methods of Calculating Index Number
• Consumer Price Index (CPI) or Cost of Living Index Number: Construction of Consumer Price Index|Difficulties and Uses of Consumer Price Index
• Methods of Constructing Consumer Price Index (CPI)
• Wholesale Price Index (WPI) | Meaning, Uses, Merits, and Demerits
• Index Number of Industrial Production : Characteristics, Construction & Example
• Inflation and Index Number

Important Formulas in Statistics for Economics

• Important Formulas in Statistics for Economics | Class 11

What is a Diagram?

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. A diagram is a visual presentation of statistical data to highlight the basic facts and relationships inherent in the data . As a diagram attracts the attention of the viewer and helps to easily grasp the information, it is appreciated by everyone. 

Table of Content

A. one-dimensional diagrams or bar diagrams, 1. simple bar diagram, 2. multiple bar diagram, 3. sub-divided bar diagram, 4. percentage bar diagram, 5. broken-scale bar diagram, 6. deviation bar diagram, b. pie diagram.

Different types of diagrams can be used to present the data. The selection of the diagram is decided by the nature of the data, the objectives of the presentation, and the abilities and experience of the presenter.

( Note: In this article, we will be covering only one-dimensional diagrams and pie diagrams.)

One-dimensional diagrams are those that have only one-dimensional measurements, such as height or length.

• In these diagrams, the magnitude of the characteristics is shown by the length or height of the bar.
• The width of a bar is arbitrarily set to make the constructed diagram more elegant and attractive.
• The length and height of the bars vary depending on the variable value. However, the width of the bar remains constant.
• Width is also determined by the number of bars that must be accommodated in the diagrams.
• If there are a large number of items, lines can be used instead of bars.
• The bars must be equidistant from one another.
• Bars can be drawn horizontally or vertically. They are, however, usually in vertical form.

The different types of One-Dimensional Diagrams are as follows:

• Simple Bar Diagram
• Multiple Bar Diagram
• Sub-Divided Bar Diagram or Component Bar Diagram
• Percentage Bar Diagram
• Broken-Scale Bar Diagram
• Deviation Bar Diagram

A diagram in which each class or category of data is represented by a group of rectangular bars of equal width is known as a Simple Bar Diagram . It is the simplest type of bar diagram. In this diagram, each bar represents one figure only. The number of bars will be equal to the number of figures. These diagrams show only one characteristic of the data, such as sales, production, or population figures for various years.

The magnitude of data is determined by the bar’s height (or length). The lower end of the bar touches the base line; therefore, the height of a bar starts from the zero unit. These diagrams can be vertical or horizontal in layout:

• Vertical Bar Diagram: The diagram in which the magnitude of the data is presented vertically, i.e., along the Y-axis, is a Vertical Bar Diagram.
• Horizontal Bar Diagram: The diagram in which the magnitude of the data is presented horizontally; i.e., along the X-axis is a Horizontal Bar Diagram.

The bars of a bar diagram can be visually compared by their relative height, and data can be easily comprehended accordingly.

Example: Present the following data in the form of a simple (vertical and horizontal) bar diagram.

Solution:  

The Multiple Bar Diagram is used to compare two or more variables such as revenue and expenditure, import and export for different years, marks obtained in different subjects in different grades, and so on. It is often referred to as a Compound Bar Diagram . The method for creating multiple bar diagrams is the same as for creating a Simple Bar Diagram. However, to distinguish the bars from each other, different bars are differentiated by different shades or colours.

Example: Represent the following information showing the number of students that use mobile phones from Realme, Redmi, and OnePlus in College A, College B, and College X,  using a multiple-bar diagram.

Solution : 

In these diagrams, the bar corresponding to each phenomenon is divided into several components. Each part or component occupies a proportional part of the bar to its share in the total.  For example, the bar corresponding to the number of students enrolled in a course can be further sub-divided into boys and girls.

• When preparing a sub-divided bar diagram, the various components in each bar should be kept in the same sequence.
• It is important to use different colours or shades to differentiate between different components.
• A suitable index should explain these various colours or shades.
• These diagrams are quite useful for comparing the sizes of various parts and throwing light on the relationship between these integral parts. For instance , such diagrams are used to present data such as sales profits from various products, a family’s expenditure pattern, the budget outlay for receipts and expenditures, and so on.

Example: Represent the following information using a sub-divided bar diagram, showing the number of students that use mobile phones from Realme, Redmi, and OnePlus in College A, College B, and College C.

A Percentage Bar Diagram is a sub-divided bar diagram that indicates the total percentage of each component rather than the magnitude. The absolute magnitudes of several components are presented using a subdivided diagram. These magnitudes can be converted into relative values by describing them as a percentage of the total.

Each data component is expressed as a percentage of the corresponding total. Thus, in a percentage bar diagram, all of the bars are of height 100, while the different segments of the bar representing the various components vary in height depending on their % value of the total. Just like in the sub-divided bar diagram, in the percentage bar diagram, different components can be differentiated by different shades or colours.

Example: Show the following information with the help of a percentage bar graph.

This diagram is used when the value of one variable is extremely high or extremely low in comparison to others. Larger bars may be broken to make space for the smaller bars of the series. Every bar has its value written on the top of the bar.

When the majority of the data figures are of low magnitude and one or more of the figures are of unusually large magnitude, a broken-scale diagram is used to present the data.

Example: Prepare an appropriate diagram using the following data from company imports in different years.

These diagrams are used to represent net changes in data such as net profit, net loss, net exports, net imports, etc.

• In these diagrams, only changes are shown, not the original data.
• The values in these diagrams might be both positive and negative.
• Positive values are displayed above the X-axis (Base line), while negative values are displayed below it.

Example : The following data shows the sale proceeds and the cost of a firm in different years. Use a deviation bar diagram to represent the profit/loss made by the firm.

A circle can be divided into parts to show the ratios of different components. A pie diagram is one such representation. Pie charts are also referred to as Angular Circle Diagrams . The circle is divided into as many sections as there are elements by drawing straight lines from the centre to the circumference. 

While preparing a pie diagram, different sectors, which represent different component elements, should be identified from one another through varied shades and colours or by using either expressive or descriptive labels.

Draw a pie chart to reflect the following expenditure for an ordinary working-class family.

According to the degrees of angles at the centre, the circle is divided into five parts. Hence, the pie diagram for the given data will be represented as:

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Diagrammatic Presentation of Data: Bar Diagrams, Pie Charts etc.

The compilation of this Presentation of Data  Notes makes students exam preparation simpler and organised.

Diagrammatic Presentation of Data

Nowadays a lot of emphasis is laid upon exceptional presentation of data. All of this is because, when presented diagrammatically, data is easy to interpret with just a glance. In such a case we need to learn how to represent data diagrammatically via bar diagrams, pie charts, etc.

Bar Diagrams

As the name suggests, when data is presented in form of bars or rectangles, it is termed to be a bar diagram.

Features of a Bar

• The rectangular box in a bar diagram is known as a bar. It represents the value of a variable.
• These bars can be either vertically or horizontally arranged.
• Bars are equidistant from each other.
• Each bar originates from a common baseline or a common axis.
• The width of bars remains the same but the height changes, according to the value of a variable, to denote the difference between their values.
• Unless they are in a specific order, the convention is that bars can be arranged in an ascending or descending order.

Types of Bar Diagrams

Simple Bar Diagram These are the most basic type of bar diagrams. A simple bar diagram represents only a single set of numerical data. Generally, simple bar diagrams are used to represent time series data for a single entity.

Generally, the Y-axis contains markings which represent the range of the value of the variable whereas the X-axis contains divisions for entities like years, time periods, areas, etc.

Multiple Bar Diagram Unlike a single bar diagram, a multiple bar diagram can represent two or more sets of numerical data on the same bar diagram. Generally, these are constructed to facilitate comparison between two entities like average height and average weight, birth rates and death rates, etc.

Separate sets of numerical data are differentiated with the help of colour variation. By the same token of simple bar diagrams, multiple bar diagrams also have divisions on the Y-axis and X-axis that represent different values of the variable and entities like year, areas etc. respectively. Note that each division on X-axis has two or more bar diagrams each according to the specified number of bars.

Sub-divided or Differential Bar Diagrams Sub-divided bar diagrams are useful when we need to represent the total values and the contribution of various sections of the total simultaneously. The different sections are shaded with different colours in the same bar.

For example, such a bar diagram can be used to represent the varying levels of employment over the years in India and each bar can be divided into two sectors, the urban and rural. Again, here the Y-axis and X-axis represent the same values as in simple and multiple bar diagrams.

Percentage Bar Diagrams This is derived further from the subdivided bar diagrams. In this, each bar has the same height that represents 100 percent of the Y-axis in totality. Further, each bar is divided into sections based on percentages calculated according to the contribution of these sections.

Percentage bar diagrams are used when the values are really high. This is because using subdivided bar diagrams in such cases would not be easy and appropriate.

Deviation Bar Diagrams Lastly, the deviation bar diagrams are the most interesting of the lot. In such a type of bar diagram, there are both negative and positive values on the y-axis. The deviation bar diagrams are used to compare the net deviation of related variables with respect to time and location.

For example, it can be used to represent a bar diagram for savings (represented by positive deviations) and deficit (represented by negative deviations) over years.

Pie or Circular Diagrams

In addition to bar diagrams, pie diagrams are also widely used to pictorially represent data. In this, a circle is divided into various segments which are decided on the basis of percentages. Which means the circle is divided into sectors depending on various percentages.

These sectors are differentiated with the help of colours. Pie diagrams have an edge over bar diagrams because they can easily provide an overview and provides a better sense of the contributions of each part. The steps for the construction of a pie diagram are:

1. The first step involves finding out the respective percentages. This is done by a simple mathematical formula to find out percentages which are–

{(Parts for the respective sector)/total parts) × 100}.

For example, if in a class of 1oo students, 30 are obese, 20 are fat and 50 are slim then the percentages will be as follows: (30/100) × 100 = 30% (20/100) × 100 = 20% (50/100) × 100 = 50%

2. A circle comprises 360 degrees. The angles that each sector will span across is decided by the given formula: (Percentage value/100)×360°

3. Finally, just plot these values according to their respective angles on a circle and give appropriate markings to complete the pie chart.

Question: Which among the following is not a feature of a bar in the bar diagram? A. The width is the same but the heights are generally different B. They are rectangular in shape C. Bars should not be equidistant D. Each bar originates from a common baseline Answer: Of all the above options, option “C” is incorrect because conventionally the bars should be equidistant.

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2: Graphical Representations of Data

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In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs.

• 2.1: Introduction In this chapter, you will study numerical and graphical ways to describe and display your data. This area of statistics is called "Descriptive Statistics." You will learn how to calculate, and even more importantly, how to interpret these measurements and graphs. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs. Our emphasis will be on histograms and box plots.
• 2.2: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs A stem-and-leaf plot is a way to plot data and look at the distribution, where all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends.  A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories.
• 2.3: Histograms, Frequency Polygons, and Time Series Graphs A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets. A frequency polygon can also be used when graphing large data sets with data points that repeat.
• 2.4: Using Excel to Create Graphs Using technology to create graphs will make the graphs faster to create, more precise, and give the ability to use larger amounts of data. This section focuses on using Excel to create graphs.
• 2.5: Graphs that Deceive It's common to see graphs displayed in a misleading manner in social media and other instances. This could be done purposefully to make a point, or it could be accidental. Either way, it's important to recognize these instances to ensure you are not misled.
• 2.E: Graphical Representations of Data (Exercises) These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/[email protected] .

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4 Diagrammatic and Graphical Representation of Data I

Dr. Harmanpreet Singh Kapoor

 Learning Objectives

• Introduction.
• Frequency Distribution
• Use of Diagrammatic and Graphical Presentation of the Data
• Suggested Readings

    1. L earning Objectives

In this module, a complete explanation about different types of diagrammatic representation of data will be discussed. This module helps one to learn different methods of diagrammatic presentation and their properties. Through this module, one can learn about which method of representation is appropriate under what type of conditions. Questions with answers are included to give an in-depth knowledge of the topic.

2.   Introduction

Statistics is a science that is based on description of data either numerically or diagrammatic or other way. This science is used to extract information from the data based on the objective. Data can be in quantitative form as well in qualitative form. Data are collected from the resources of study and are available in raw form. After collecting and editing the data the next stage is to organize the data. Classification and tabulation of the data are among the most important tools for the precise, clear and comprehensible representation of the data. However, sometimes these forms of presentation are not appealing to the common person. Due to technicality involved in these forms, it may not be interesting for a common person to be able to understand the things in a simple manner. Another way to represent the data is through diagram and graphs that present the data into attractive manner that appeal more to the mind of the spectators. These forms are more attractive, fascinating and impressive than the other methods. The best part of diagrammatic representation method is that even a layman person can understand this without any previous knowledge of statistics. This is the reason that diagrams and graphs are used to give basic education to the kids.

Another important feature of the diagrammatic and graphical representation is that it saves lot of time as these are easy to build up and one can draw meaningful inference from them. These methods are able to present that information that might be lost amid the details of classification and tabulation of data. These methods also facilitate the person for comparing the value of two or more sets of data. Graphs and charts are used to clarify a complex problem and reveal the hidden facts that are not clear from the tabular form. Hence, graphs and diagrams are important not only for the representation of the data but for visual comparison of two or more datasets. Now in the next section, a brief introduction about frequency distribution and how to form it will be discussed.

    3.  Frequency Distribution

In English language, frequency means the rate of occurrence of something in a repetitive manner in a particular time interval or time frame. Statistics is concerned with the extraction of information from the numbers collected in a raw form from the study. We already discussed about definition of variables in the second module.

In practical life, variables are used to represent these numbers in case of quantitative data like in a study of sales of luxury cars in a particular region in a year. One can consider “the sale of a car in a day” as a variable and note down the sale of a car in a day by variable where i=1,2,…..365. Here the values, 1, 2, … . . 365 represent the sales of a car in the first day of a year or financial year and similarly second day of the year and so on. The values of 1, 2, … . , 365 are known as the values of the variable.

Frequency of a value of the variable means the number of times a same value is repeated in the whole dataset. For example, if we assume that the no. of sales of a car are 2 units on 10th day, 3 units on 20th day, 2 units on the 45th day, 4 units on the 70th day of the year and so on. Here, 2 units appear two times, 3 and 4 units appear single time from the available information. So, from the available information the frequency of sale of 2 cars per day is two and other has only one. With an increase in the available information, one can construct frequency table that represent the repetition of the values in a dataset.

For example, let us consider the observation of sales of car in the month of February (28 values). These are 2, 3, 1, 2, 4, 5, 3, 2, 1, 3, 5, 6, 1, 2, 4, 2, 3, 5, 1, 3, 4, 2, 3, 5, 4, 1, 4, 2

Table No. 1

In the above table, we observe that for seven days two units of cars are sold, for six days three cars are sold and so on. Hence one can form the frequency table by counting the same observations in the data set this means frequency of a value of a variable is the number of times it occurs in a given series of observations. The table that represents the frequency of the value side by side is called frequency table . There are two forms of frequency distributions- Ungrouped frequency distribution and Grouped frequency distribution.

To understand the difference between two methods, we consider a data set of IQ score of 30 students and construct ungrouped and grouped frequency distribution.

Table No. 2

3.1 Ungrouped Frequency Distribution

Ungrouped frequency distribution table shows the frequency of the values in the dataset on individual basis. Table no. 3 is an example of ungrouped frequency distribution as the first column in the table represents the observations and second column shows corresponding frequency.

From Table No. 3, one can observe that 2nd column and 4th column show the frequency values of the dataset (from Table No. 2). Hence in ungrouped frequency distribution, the values of the dataset are shown on individual basis.

3.2 Group Frequency Distribution

In this method, the values of the variables are shown in the group or interval. In the following table, observations from Table no. 2 are used to present them in group frequency distribution. The smallest observation in the dataset is 35 and maximum value is 94. In Table no. 4, we consider width of the interval as 10 and lowest class value as 30 and so on till we cover the maximum value in the dataset. In the next section, we will discuss about how to choose, type of class, class interval, width of class interval etc.

From Table No. 4, we can see 70-80, 80-90 intervals have maximum frequency value that is 8. Hence we can conclude that IQ score of the most of the students lie between70 to 90.

On the comparison of Table No. 3 and Table No. 4, one can see that group frequency distribution visualize the important characteristics of the data in a simple and understandable manner about the tendency of IQ score of students over ungrouped frequency distribution.

Steps for forming a group frequency distribution

Many techniques are used for the formation of the group frequency distribution. For group of observations, we divide the data into class intervals and difference between upper and lower interval is called the width of the class interval. There are few points that must be kept in mind while preparing a group frequency table.

(a) C lass type : One should define class type in a very clear manner. It should be exhaustive and mutualy exclusive so that variable’s value must be assigned to only one class in the table.

(b)  Class Intervals: It means how many intervals should be formed for the available data. Number of intervals depend on the things like number of observations in the data, its magnitude value, level of precision and further analysis of the data.

The most common formula that is used for the determination of the interval in the group frequency distribution is Sturge’s rule:

k= 1 + 3.322 log 10 N

where is the number of classes and N is the total number of observations in the data. This rule is used for correct determination of intervals in the data and it is further used for the determination of the width of the class interval.

(c) Width of class interval: Width of the interval means the difference between the lower limit and upper limit of the interval. The width of the interval is defined through the formula that is ℎ = Range/No. of Classes

where ℎ denote the width of the class interval and range is defined as the difference between the highest and lowest value of the data set.

(d)  Class limits methods: There are different methods that are used for the classification of the data set on the basis of class interval. The limit consists of two numbers that are used for the purpose of tallying observations into various classes. There are two different methods for the classification of the data on the basis of class intervals. These are:- (a) Inclusive method and (b) Exclusive Method.

(i)  Inclusive method: In inclusive method, the upper limit of a class interval is considered in the interval itself and is not related with the next class. For example, in inclusive method, the class limits are 0-4, 5-9, 10-14, 15-19 and so on. Hence one can see that both the upper and lower limits are included in the class and thus it is termed as inclusive. The main drawback of this method for continuous data observations for example if data value is 4.5 then with this method one cannot tabulate or assign the value to any interval.

(ii)  Exclusive method: In this method, the data are classified into class interval of such time that upper limit of one interval is the lower limit of next succeeding class interval. For example, in exclusive method the class limits should be of such type that is 0-5, 5-10,10-15 and so on. Hence all those values that are less than 5 are considered in first interval and  all those data values that are above than 5 but less than 10 are counted in second interval.  Hence in exclusive method, the problem of inclusive method is taken care of.

(e)  Mid value or Mid points: Mid value is calculated by taking the sum of upper and lower limit of the interval and dividing that sum by 2. This value is used as a representative value of the class interval and it is used for evaluation of mean, median, mode and higher moments of the data.

    In the next section, we will discuss about cumulative frequency distribution and how to construct it.

3.3 Cumulative Frequency Distribution

We have already discussed about the frequency distribution in the previous section. Frequency distribution counts the occurrence of the same value in the data but sometime one is interested in the number of observations that are small or greater than a given value. In such type of situation, one has to calculate the accumulated frequency less than or greater than some specified value. This accumulated value is known as Cumulative frequency distribution.

The frequency of observations till a given value is considered as less than cumulative frequency and the frequency of observations that are greater than a value is called more than cumulative frequency.

Using the same observation as given in Table No.4. The cumulative frequency distribution for both more and less than are given in the following table.

Table No. 5

From the above table, one can see the less than and more than cumulative frequency values of the data. These values are further used for graphical representation of the data. For example, ogive curve of more than and less than type use these values for plotting on the axis.

4.  Use of Diagrammatic and Graphical Presentation of the Data

Diagrammatic and Graphical presentation of the data are useful in practice due to the following reasons.

(1)   The information that we acquire from the graphical and diagrammatic representation of the data is easy to understand even for a layman person due to its simplicity.

(2)   People are more interested in graphical presentation of facts then just numbers due to eye caching effect of diagram or pictures.

(3)   Graphs and picture can simplify the complexity of the data that cannot be easily be understood with the figures.

(4)   With the graphical presentation, one can easily compare the statistical data relating to different time and places to bring out the hidden facts and relationship among the statistical variables.

There are some limitations of diagrammatic and graphical representations like they do not show the details behind the numbers that can only be shown from the table in a better way. A single diagram or graph does not have a great importance rather than it is used for comparison purpose with other diagram or graph. In the next section, difference between graph and diagram will be discussed so that reader can understand the difference between them in a clear manner and use them at their proper place without any confusion.

4.1 Difference between diagrams and graphs

There are few rules based on them, one can differentiate between graphs and diagram but these rules are not standard for all so there is scope of changes in these rules among different persons. But we will discuss few rules that are considered common for all. These rules are:

(a)   Diagram are plotted on the paper while graphs are plotted on a paper called graph paper graphs helps in the study of mathematical or numerical relationship between variables but in diagram precise relationship among variables are not discussed.

(b)   In diagram , different tools like bars, rectangles, circles etc are used to present the information in the data. Whereas in graphs, different tools like lines, dots etc are used to present the data.

(c)   Diagrams only give approximate information regarding the data as this information will not be used further for analysis purpose. On the other hand, graphs give more precise, accurate information about the data and they are used for further analysis purpose.

(d)   Diagrams are used for the presentation of the categorical and geographical information in the data. On the other hand, graphs are used for the presentation of the time series and frequency distribution.

(e)   Diagrams are more eye catching than graphs. Also diagrams are used for the understanding of the layman person but graphs are used by experts from the field for the further analysis of the information.

(f)  Graphs are easier to build than comparative to the diagram.

There are few points based on which one keep in mind while constructing the diagrams. These are:-

• Diagram gives only a pictorial representation of the quantitative data for rough guesses;
• it can only be used for homogenous data;
• it is not reliable to make further inference about the data.

   So, basically diagram are used for the graphical interpretation purpose only. One cannot use it to find out reasons or inference from the data.

While constructing diagrams, there are some general rules that should be followed. These are:-

• An appropriate diagram can only present the data in a better way. Thus, it is essential to choose the right diagram for the data that need expertise as well as knowledge. It may be possible that due to inappropriate selection of diagram the interpretation might be wrong that can lead to unbearable results.
• It is also important that a diagram should have an appropriate title corresponding to the nature of the data. With an appropriate title, a person can understand the main idea in the diagram.
• It should be constructed in such a way that it portray all the relevant information within an allotted space. So, it should be appropriate in terms of size and consistent in terms of dimensions.
• It should be neat, clean with footnotes and proper indexing that will attract the interest of the common man.

    In the previous section, we discuss the characteristics of the appropriate diagram. Now in the following section, a brief note on different types of the diagrams will help to understand it importance.

4.2 Types of Diagrams

There are many types of diagram based on it dimensionality. These are

(i) One dimensional diagrams

(ii) Two dimensional diagrams

(iii) Pie Chart

(iv) Three dimensional diagrams

Each type of diagram is used for specific type of data i.e. for complex data, one need more dimensions to see the impact of one factor on the other. Hence the choice of the type of the data depends on the nature of the data. One dimensional diagram is discussed here to give elementary knowledge. One can read other dimensions diagram also from the references.

One dimensional diagrams

These types of diagram use only one dimension i.e. only length of bars and lines are taken into account. So, these diagrams are known as one-dimensional diagrams. Bars may be vertical or horizontal. Vertical bars are mostly used to represent growth or decline rate of the variable under study while horizontal bars are used to represent the data of attributes. There are few points that should be kept in mind while using bars.

(a) Bars should be constructed within an allotted space and of uniform shape and size. (b) Scale should be chosen according to the magnitude of the observations. (c) Bars must have the same base line for a given data. (d) It is better to represent the value at the top of the bar for the convenience of the reader. (e) Bars should be arranged from the left to right in order of magnitude for consistency.

The following example help you to understand the point given above.

The following data give the approximate average yield of rice in kg. per acre in different state of a country during a 2000-2001.

From the above figure, one can observe that the above diagram satisfies all the conditions. Hence one can easily understand the characteristics or facts of the data through diagrams in an easy manner.

Self- Checked Exercise

Question What are the benefits of using diagrammatic and graphical representation of the data?

Ans With the help of diagrammatic and graphical representation of the data even a layman person can understand the facts related with it. Although these techniques are not helpful to explain hidden factors influencing the variables or data.

Question How diagrammatic and graphical representation help in understanding the information contained in the data?

Ans As we are aware of the fact that one can understand the diagram or graphs in a better way than just numbers. Hence, one can easily understand the information contained in the data by using graphical and diagrammatical representations.

Question How graphical representation is different from diagrammatic presentation?

Ans In diagrammatic mode of presentation, one can use the devices like bars, rectangle etc whereas in graphical methods, one can use points, lines of different kind etc to present the information.

Data are collected from the resources of study and they are available in raw form. Thus after collecting and editing the data the next stage is to organize the data. Classification and tabulation of the data are among the most important tools for the precise, clear and comprehensible representation of the data. Frequency distribution and its various forms are discussed in the module. Graphical and diagrammatically forms and differences between them are discussed. Various forms of diagram one-diagram, two dimensional etc. are also used to represent the data in an understandable manner.

6. Suggested Readings

Agresti, A. and B. Finlay, Statistical Methods for the Social Science, 3rd Edition, Prentice Hall, 1997.

Daniel, W. W. and C. L. Cross, C. L., Biostatistics: A Foundation for Analysis in the Health Sciences, 10th Edition, John Wiley & Sons, 2013.

Hogg, R. V., J. Mckean and A. Craig, Introduction to Mathematical Statistics, Macmillan Pub. Co. Inc., 1978.

Meyer, P. L., Introductory Probability and Statistical Applications, Oxford & IBH Pub, 1975.

Triola, M. F., Elementary Statistics, 13th Edition, Pearson, 2017.

Weiss, N. A., Introductory Statistics, 10th Edition, Pearson, 2017.

One can refer to the following links for further understanding of the statistics terms.

http://biostat.mc.vanderbilt.edu/wiki/pub/Main/ClinStat/glossary.pdf

http://www.stats.gla.ac.uk/steps/glossary/alphabet.html

http://www.reading.ac.uk/ssc/resources/Docs/Statistical_Glossary.pdf

https://stats.oecd.org/glossary/

http://www.statsoft.com/Textbook/Statistics-Glossary

https://www.stat.berkeley.edu/~stark/SticiGui/Text/gloss.htm

https://stats.oecd.org/glossary/alpha.asp?Let=A

Essential Graphical Techniques in Geography pp 153–191 Cite as

Diagrammatic Representation of Geographical Data

• Swapan Kumar Maity 3  
• First Online: 30 November 2021

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Part of the book series: Advances in Geographical and Environmental Sciences ((AGES))

Diagrammatic representation and visualization of geographical data is very simple, attractive and easy to understand and explain to the geographers as well as to the common literate people. It helps to explore the nature of data, the pattern of their spatial and temporal variations and understanding their relationships to accurately recognize and analyse features on or near the earth’s surface. This chapter focuses on the detailed discussion of various types of diagrams classified on a different basis. All types of one-dimensional (bar, pyramid etc.), two-dimensional (circular, triangular, square etc.), three-dimensional (cube, sphere etc.) and other diagrams (pictograms and kite diagram) have been discussed with suitable examples in terms of their appropriate data structure, necessary numerical (geometrical) calculations, methods of construction, appropriate illustrations, and advantages and disadvantages of their use. It includes all the fundamental geometric principles and derivation of formulae used for the construction of these diagrams. A step-by-step and logical explanation of their construction methods becomes helpful for the readers for an easy and quick understanding of the essence of the diagrams. Each diagram represents a perfect co-relation between the theoretical knowledge of various geographical events and phenomena and their proper practical application with suitable examples.

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Sarkar A (2015) Practical geography: a systematic approach. Orient Blackswan Private Limited, Hyderabad, Telengana, India. ISBN: 978-81-250-5903-5

Sharma PD (1975) Ecology and environment. Rastogi Publications, Gangitri, Shivaji Road, Meerut-250002, ISBN: 978–93–5078–122–7

Singh RL, Singh RPB (1991) Elements of practical geography. Kalyani Publishers, New Delhi

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Commerce Aspirant » Economics Class 11 » Presentation of data class 11

Presentation of data class 11

Presentation of data class 11 notes are presented in this post for easy access to the students. By taking these notes, you can stay active and engaged throughout your reading, revision, and lectures. They also help with clear thinking and understanding. Choose the most important ideas to focus on. These notes provide a useful record of important information and its sources. You’ll be able to recall better what you heard with these notes.

• Presentation of data
• Textual Presentation
• Objective of Tabulation

Parts of a table

• Types of table
• Diagrammatic and Graphical Presentation
• Steps to construct pie diagram
• Bar Diagram

Limitations of diagrammatic presentation

• Advantages of graphical presentation
• Functions of a graph

Frequency Diagram

Arithmetic line graph, presentation of data class 11 .

The presentation of data in such a clear and appealing manner that it is simple to comprehend and analyse is referred to as “data presentation.”

Methods of presentation of data

• Textual or descriptive presentation
• Tabular presentation
• Diagrammatic presentation
• Graphic presentation

Textual Presentation under Presentation of data class 11 

Data are presented in the form of text or textual or descriptive presentation. This works well when the amount of data isn’t too big.

For example; The number of boys in class 10th A was 320, out of which 200 were from the humanities section.

• The only limitation it has is that one needs to go through the entire text for comprehension.

Tabular Presentation

In a tabular presentation, data becomes a part of any study, description, or text or becomes a matter of study. When numerical data is presented in a systematic way in rows and columns it is called tabulation.

Objectives of Tabulation under Presentation of data class 11 

• Tables aim to present the classified data in an orderly way. The idea behind this is to simplify the complex data.
• Tabulation is very important to save space by providing the data in a meaningful manner.
• Tabulation facilitates quick comparisons among total observations.
• Tabulation is a phase between a classification of data and its presentation. Therefore statistical analysis becomes easier when it comes to Tabulation.
• Numbers and data can be easily identified in providing references.
• Title; The title of the table should be attractive and informative.
• Size; The size of the table should be manageable.
• Attractive presentation; A table should be appealing to the eye.
• Suitable purpose; A table should stick to its statistical information.
• Simple; It should be easy to comprehend.
• Comparison of data; The data that needs to be compared should be placed in columns and rows.
• Columns and rows; The columns and rows should be numbered for reference.
• Clarity; A table should be complete and self-explanatory.
• Units; The units of the variables should be specified, such as Price In ₹, weight in kg.

Classification of Data and Tabular Presentation

• Qualitative Classification of Data and Tabular Presentation; This occurs when data is classified on the basis of qualitative attributes.
• Quantitative Classification of Data; This occurs when data are classified based on the quantitative characteristics of a phenomenon.
• Temporal Classification: Data are categorised using a temporal classification system, with time serving as the classifying variable.
• Spatial Classification; Location takes on the role of the classifying variable in spatial classification. It could be a district, a town, a village, etc.

  Types of Tables under Presentation of data class 11 

• Classification by Objective or Purpose These tables are divided into two categories:
• Table for All Purposes: A General Purpose Table covers a wide range of information on the same topic and provides a detailed representation of the raw data. The data are presented without any particular analytical purpose. These tables typically have a large size and are typically included for reference in the appendix. There are numerous applications for these tables. They are used a lot in the government departments’ reports. Other names for it include “Reference Table” and “Repository Table.”
• Table for Special Purposes: These tables give data intended for a specific enquiry. Take, for instance, a company’s annual production figures. The results of data analysis are presented in these typically brief tables. Other names for it include “Text Table,” “Summary Table,” and “Analytical Table.”

2. Classification Based on the Nature of the Data Based on the nature of the data’s originality, there may be two types of tables:

• The initial table: The statistical data are presented in their original form in the Original Table, i. There is no rounding of the numbers in this kind of table. It contains information that was initially gathered from the primary source. Other names for it include “Primary Table” and “Classification Table.”
• Table Derivative: a table that displays averages, percentages, ratios, and other derived results from the original data, is referred to as a Derived Table. It conveys the data gleaned from the primary or original tables. A “Derivative Table” is another name for it.

3. Classification Based on Extent of Coverage Tables can be of two types depending on the extent of coverage (or construction):

• Plain Table: The simplest form of a table, this one presents data in accordance with a single characteristic. Since only one variable is being investigated, the univariate frequency distribution is presented in a one-way table. Other names for it include “One-way Table” and “First Order Table.”
• The Double or Two-Way Table: It details two aspects of a particular phenomenon that are interconnected. The table, for instance, would transform into a two-way table if the numbers of Class XI students in various sections were further divided according to gender.
• Treble Table, or three-way table: Three data characteristics are categorized in a three-way table. It details three characteristics of a particular phenomenon that are connected to each other. A three-way table would be required in the case of the two-way table if the students were further divided into day-scholars and hostellers.
• Table of Manifolds: Manifold Table is the name of the table that describes more than three data characteristics. Numerous interrelated issues or characteristics of a given phenomenon are described in these tables. A table in this form is the most complicated.

Diagrammatic and Graphical Presentation under Presentation of data class 11 

Diagrammatic presentation of data refers to the process of presenting data straightforwardly and appealingly.

• These transform the extremely abstract concepts contained in numbers into a form that is more tangible and simpler to comprehend.

Merits of Diagrammatic presentation

Diagrams give a bird’s eye-view of the whole mass of statistical data and are extremely usefu and significant. The following are some of the benefits or applications of diagrammatic presentation:

• Diagrams are eye-catching and powerful: Even a layperson can be drawn to data that is presented in the form of diagrams because of their usefulness and advantages. As a result, diagrams attract more attention than figures do. In everyday life, while reading newspapers, magazines, and other publications, We mostly look at the diagrams, but we skip over the figures. As a result, diagrams are frequently used in public events like board meetings, conferences, exhibitions, seminars, and others.
• Attractive and impressive, easy to remember, simplifies data, cuts down on time spent making comparisons, and provides additional information 2. Simple to Recall: Diagrams help people remember a lot. Compared to figures presented in tabular form, the mental image created by diagrams lasts significantly longer.
• Data is simplified by diagrams: Diagrams are used to simplify and make easy-to-understand representations of huge amounts of complex data.
• Diagrams are time-saving: The complicated mass of data is simplified by diagrams. Therefore, data that is presented in the form of diagrams is easy to comprehend. However, it takes a lot of time to analyze the significance and trend of large amounts of data.
• When making comparisons, diagrams are helpful: Using diagrams to display two sets of data makes it simpler to compare them. Through the use of diagrams, for instance, it is simple to compare the population growth rates of various nations.
• Universality of Application: This method can be used anywhere, at any time, and in any place. The majority of subjects and other fields employ this method.
• Diagrams provide additional data: Diagrams not only show the characteristics of the data, but they also reveal other omitted facts and relationships that cannot be determined by tabulating or categorizing the data.

Different kinds of diagrammatic presentations under Presentation of data class 11 

Pie diagram.

• Arithmetic line graph

A pie diagram, also known as a circular diagram, is a circle with various segments that represent the percentage values of a series. These diagrams do not show the exact value of the variables.

Steps to construct a pie diagram

• Using a compass, draw a circle of the right size, taking into account the size of the paper and the data to be represented.
• Make percentages of the total from the values of the various components.
• In the circle, the percentage values are converted into the appropriate degrees. Since each item’s percentage value is equal to 100 and a circle contains 360 degrees, one percentage value is represented by 100 360 degrees, or 3.6 degrees. To determine the number of angles, multiply each percentage value by 3.6.
• To draw the angles that are represented by the first component, use a radius, preferably horizontally, as the base line. The new line will serve as the foundation for the angular representation of the second component. This procedure should be repeated until each component is represented.
• For proper identification, depict various components in various shades, designs, or colours .

Bar Diagram under Presentation of data class 11 

Bar diagrams are diagrams in which data are shown as bars or rectangles.

There are four types of Bar Diagrams;

Nowadays, diagrams enjoy a lot of popularity. However, despite their utility, they are constrained in some ways. The following are the restrictions:

• Experts will not benefit: Diagrams only provide a hazy understanding of the issue, which may be useful for the average person but not for an expert who wants a precise understanding.
• Limited Details: The information provided by diagrams is limited and approximate. We must refer to the original statistical tables for comprehensive and precise data.
• They can only be used in comparison studies: Only when comparisons are desired are diagrams useful. A single diagram is not very important. It can only be interpreted in conjunction with another diagram that can be used as a comparison.
• Easy to Misuse: Diagrams are susceptible to easy misuse. If the wrong kind of diagram is used, it will draw false conclusions. As a result, one should always take precautions against them.
• Lack of Additional Research: Diagrams cannot be investigated further.
• Impossible Presentation with a Minute Difference: Diagrams fail to reveal minute variations in large figures (observations). Diagrams only show values with a very low level of precision. For instance, if two significant figures, such as 8,560 and 8,500, are depicted in a diagram, the difference will not be very obvious.

Graphic presentation under Presentation of data class 11 

Advantages of graphic presentation.

The following are the main advantages of using graphics to present data:

• Impressive and appealing: Compared to tables of figures, graphs are always more attractive and impressive. Graphs can explain a fact that is hard for the average person to comprehend. As a result, the expression “a picture is worth a thousand words” applies.
• Data presented in a way that is easy to comprehend: Graphs assist in simplifying and comprehending complex data. Both the observer and the statistician benefit from the time and effort saved.
• Using as a comparison: Graphs make it simple to compare two or more phenomena.
• Where the positional averages are: Positional averages like the median, mode, and quartiles can be found using graphs.
• No need to be proficient in mathematics: Because they are so straightforward and straightforward, comprehending the graphs does not necessitate a great deal of technical knowledge. It’s easy for even a layperson with no mathematical background to understand.
• Contributing to Predictions: Trends that could occur in the near future can be better predicted using graphs.
• Benefit for all: Graphs can now be used in a variety of fields, including trade, economics, government agencies, advertising, and more.

Functions of Graph under Presentation of data class 11 

• To make complex data simple.
• To make comparisons easy.
• To check on accuracy.
• To make more penetrating analysis.

Types of Graphs under Presentation of data class 11 

Frequency diagrams like the histogram, frequency polygon, frequency curve, and ogive are typically used to represent data that is composed of grouped frequency distributions.

Two types of Histogram frequency distribution are;

• Histograms of equal class intervals
• Histograms of unequal class intervals.

• The less than method, adds the frequencies corresponding to each upper limit of the series starting with the upper limit of the first values.
• More than Method: We take the cumulative total of the frequencies starting with the lower limit of the first class interval in this method.

Line Frequency Graph; They are used to depict discrete series.

An arithmetic Line graph is also known as Time series; This graph plots time (hour, day, date, week, month, and year) along the X-axis and the variable’s value along the Y-axis.

There are two types of arithmetic line graphs.

Limitations of graphic presentation under Presentation of data class 11 

The following are the drawbacks of graphic presentation:

• Application Limitations: They are primarily intended to inform the general public about quantitative facts. Graphic presentation is of little use to experts.
• It’s possible to misuse them: A significant variation in the graph’s shape may result from a minor challenge or measurement error. As a result, it may result in false positives. Even biased individuals can use it to present a false narrative.
• Subjective: In nature, graphs are subjective. Each person’s interpretation is different.
• Lack of Precision: The precision of the data is not shown by graphs. They only display data fluctuations. As a result, they are not suitable for testing the data’s accuracy.

  Presentation of data class 11 notes give a wholesome definition of presentation and various related concepts. You can stay active and engaged throughout your reading, revision, and lectures by taking these notes. Additionally, they aid in clear thinking and comprehension. Selectively identify important ideas. A useful record of important information and its sources can be found in these notes. These notes will help you remember what you heard better.

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DIAGRAMMATIC REPRESENTATION OF DATA

An attractive representation of statistical data is provided by charts, diagrams and pictures.

Diagrammatic representation can be used for both the educated section and uneducated section of the society. Furthermore, any hidden trend present in the given data can be noticed only in this mode of representation.

However, compared to tabulation, this is less accurate.

So if there is a priority for accuracy, we have to recommend tabulation.

We are going to consider the following types of diagrams :

1. Line diagram

2. Histogram

3. Bar diagram

4. Pie chart

Line Diagram

When the time series exhibit a wide range of fluctuations, we may think of logarithmic or ratio chart where "Log y" and not "y" is plotted against "t".

We use Multiple line chart for representing two or more related time series data expressed in the same unit and multiple – axis chart in somewhat similar situations, if the variables are expressed in different units.

The profits in thousand of dollars of an industrial house for 2002, 2003, 2004, 2005, 2006, 2007 and 2008 are 5, 8, 9, 6, 12, 15 and 24 respectively. Represent these data using a suitable diagram.

We can represent the profits for 7 consecutive years by drawing either a line diagram as given below.

Let us consider years on horizontal axis and profits on vertical axis.

For the year 2002, the profit is 5 thousand dollars. It can be written as a point (2002, 5)

In the same manner, we can write the following points for the succeeding years.

(2003, 8), (2004, 9), (2005, 6), (2006, 12), (2007, 15) and (2008, 24)

Now, plotting all these point and joining them using ruler, we can get the line diagram. 

Showing line diagram for the profit of an Industrial House during 2002 to 2008.

A two dimensional graphical representation of a continuous frequency  distribution is called a histogram.

In histogram, the bars are placed continuously side by side with no gap between  adjacent bars.

That is, in histogram rectangles are erected on the class intervals of  the distribution. The areas of rectangle are proportional to the frequencies.

Draw a histogram for the following table which represent the marks obtained by 100 students in an examination :

The class intervals are all equal with length of 10 marks.

Let us denote these class intervals along the X-axis.

Denote the number of students along the Y-axis, with appropriate scale.

The histogram is given below.

Bar Diagram

There are two types of bar diagrams namely, Horizontal Bar diagram and Vertical bar  diagram.

While horizontal bar diagram is used for qualitative data or data varying over  space, the vertical bar diagram is associated with quantitative data or time series data.

Bars i.e. rectangles of equal width and usually of varying lengths are drawn either  horizontally or vertically.

We consider Multiple or Grouped Bar diagrams to compare  related series. Component or sub-divided Bar diagrams are applied for representing data  divided into a number of components. Finally, we use Divided Bar charts or Percentage

Bar diagrams for comparing different components of a variable and also the relating of  the components to the whole. For this situation, we may also use Pie chart or Pie diagram  or circle diagram.

Example : 

The total number of runs scored by a few players in one-day match is given.

Draw bar graph for the above data.

In a pie chart, the various observations or components are represented by the sectors of a circle and the whole circle represents the sum of the value of all the components .Clearly, the total angle of 360° at the center of the circle is divided according to the values of the components .

The central angle of a component is

=  [Value of the component / Total value] x 360°

Sometimes, the value of the components are expressed in percentages. In such cases,

=  [Percentage value of the component / 100] x 360°

The number of hours spent by a school student on various activities on a working day, is given below. Construct a pie chart using the angle measurement.

Draw a pie chart to represent the above information.

We may calculate the central angles for various components as follows :

From the above table, clearly, we obtain the required pie chart as shown below.

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