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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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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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• 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

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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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] .

Graphical Representation of Data

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

Definition of Graphical Representation of Data

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

Representation of Data

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

Principles of Graphical Representation of Data

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

Advantages and Disadvantages of Graphical Representation of Data

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

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

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

Rules of Graphical Representation of Data

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

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

Uses of Graphical Representation of Data

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

Types of Graphical Representation of Data

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

Related Topics

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

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

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

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

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

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

Hence, mode = 54

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

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

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

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

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Practice Questions on Graphical Representation of Data

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

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

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

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

What is the Use of Graphical Representation of Data?

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

What are the Ways to Represent Data?

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

What is the Objective of Graphical Representation of Data?

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

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• Diagrammatic Presentation of Data

Introduction - Diagrammatic Presentation of Data

Diagrams are an essential operational tool for the presentation of statistical data. They are objects, mainly geometrical figures such as lines, circles, bars, etc. Statistics elaborated with the help of diagrams make it easier and simpler, thereby enhancing the representation of any type of data.

What is Diagrammatic Representation of Data?

Representation of data assisted by diagrams to increase the simplicity of the statistics surrounding the concerned data is defined as a diagrammatic representation of data. These diagrams are nothing but the use of geometrical figures to improve the overall presentation and offer visual assistance for the reader. 

What are the Types of Diagrams used in Data Presentation?

The type of diagram suitable for data presentation solely depends on the particular dataset and its statistical elements. There are multiple types of diagrams used in data presentation. They can be broadly categorized in the following types of one-dimensional diagrams –

A. Line Diagram

Line diagram is used to represent specific data across varying parameters. A line represents the sequence of data connected against a particular variable. 

Properties of Line Diagram –

The Lines can be used in vertical and horizontal directions.

They may or may not have uniform scaling 

The line connecting the data points state the statistical representation of data.

Example: Arjun, Sayak and Mainak started monitoring their time of reporting for duty for a certain week. A-Line diagram to represent their observed data on average reporting time for those days would look like –

(Image will be Uploaded Soon)

So, as per the Line Diagram, it can be easily determined that Arjun reported for work mostly at 9:30 AM while Sayak and Mainak’s most frequent times of entry at work is 10:30 AM and 10:50 AM respectively. 

B. Bar Diagram

Bar Diagram is used mostly for the comparison of statistical data. It is one of the most straightforward representations of data with the use of rectangular objects of equal width.

Properties of Bar Diagram –

The Bars can be used in vertical and horizontal directions.

These Bars all have a uniform width.

All the Bars have a common base.

The height of the Bar usually corresponds to the required value.

Example: A dataset comparing the percentile marks obtained by Shreyasi and Monika in Science subjects in the examination can be represented with the help of a Bar diagram as –

From this diagram, we can easily compare the percentile marks obtained by Shreyasi and Monika in the subjects Mathematics, Physics, Chemistry and Computer Science. 

C. Pie Chart

To know what a Pie Diagram is, it is advised to brush up on the fundamentals of the geometrical theories and formula of a Circle. For the statistical representation of data, the sectors of a circle are used as the data points of a particular dataset. A sector is the area of a circle formed by the several divisions done by the radii of the same circle.

Example: In a recent survey, a dataset was created to figure how many participants of the survey thought that Tenure or Tenor is the correct spelling in the field of Banking . A Pie Chart would present the collected data as –

With the help of this Pie Chart, it can be easily determined that the percentage of participants in the survey who chose ‘Tenor’, to be the correct spelling of the word for use in the field of banking, is 25% whereas 45% picked ‘Tenure’ as the correct answer. 20% opted for both to be correct while 10% of them were not sure with their attempt.

Advantages of Diagrammatic Presentation

There are several advantages in the presentation of data with the various types of diagrams. They are –

1. Makes it Much Easier to Understand

The presentation of data with the help of diagrams makes it easier for everybody to understand, which thereby makes it easier to grasp the statistics behind the data presented. Diagrammatic data presentation is quite common in newspapers, magazines and even in advertising campaigns so that the common mass can understand what the data is trying to reveal. 

2. Presentation is Much Simpler

With the help of diagrams, presentation of extreme values – extensive unstable data as well as small complicated data complex can be simplified exponentially. 

3. Comparison Operations are More Interactive

Datasets that require comparison of their elements use the application of diagrams for representation. Not only is the presentation attractive, but it is also ideal for showcasing a comparison in statistics.

4. Accepted Universally

Every academic and professional field, let it be Economics, Commerce, Science, Engineering, Statistics, etc. make use of diagrams across the world. Hence, this metric of data presentation is universally accepted.

5. Improves the Representation of Data as a Whole

Statistics are incomplete if diagrams are tables that are not implemented for the presentation of data. Hence, the use of diagrams helps in the overall statistical concept of data representation.

Students who are looking forward to diving deep into the theories and principles of Diagrammatic representation of data, make sure to visit the official website of Vedantu and join a live online tutoring class!

Relevance of Diagrammatic Presentation of Data

Diagrams are visually pleasing and are a great way of representing any form of data. The heavy statistics that we generate can be easily represented via diagrams such as bar charts, pie charts etc. It makes the presentation look neater and more organized. They visually aid the reader in understanding the exact situation and are also very easy to look at.  They save a lot of time and confusion and have a universal utility .  All students must learn how to represent data through diagrams so that they can present facts and figures in an organized manner.

Does Vedantu have Anything on the Diagrammatic Presentation of Data?

Vedantu has ample study material on the diagrammatic representation of data. All students can read from Diagrammatic Presentation of Data and know more. This is available completely free of cost on the platform so that the students do not hesitate before accessing them.

FAQs on Diagrammatic Presentation of Data

1. Which are the types of diagrams used in data representation?

The types of diagrams used in the representation of data are line diagrams, bar diagrams, pie charts and a few others. These are used to represent facts as they make it easier for the students to understand certain information. More about this has been explained in the Diagrammatic Presentation of Data. This page has relevant information that the students can use to understand these diagrams. After having gone through this page, they will know how to represent certain information in the form of diagrams.

2. Are there any merits of the diagrammatic representation of data?

There are a couple of merits of the diagrammatic representation of data. Some of which is that it makes it much easier to understand data, the presentation is simpler, it becomes easier to compare and correlate, and it is universally accepted. 

This page has all the details that are needed by the students to know. It is always better to present data in the form of diagrams as it makes it much more systematic. An organized manner of depicting figures makes anything simpler to understand. 

3. Is a pie chart an accurate way of representing data diagrammatically?

In a pie chart, the sectors of a circle are used as the data points of a particular dataset. It is indeed an accurate method of representing data as the correct percentage can be found out. All students can check out the Diagrammatic Presentation of Data on Vedantu. This page has all the information that’s needed by the participants. The other forms of diagrams that can be utilized for data presentations have also been talked about. This page has been created by expert Commerce teachers who know the topic inside out and can be read by all those who wish to do well in the tests.

4. Difference between the Diagrammatic and Graphical Presentation of Data.

All graphical representations of data can be a diagram, but all diagrams are not a graph. Graphs are represented on a scale, but diagrams are required to be constructed to a scale. Construction of graphs requires two more axes, but none is a necessity in case of diagrams.

5. What are the different Types of Diagrams in Statistics?

The different types of diagrams used in statistics are line diagram, bar diagram, and pie chart. Bar diagrams can further be classified into simple bar diagrams, multiple bar diagrams and component or sub-divided bar diagrams.

• 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.

Suggested Videos

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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5 Diagrammatic and Graphical Representation of Data II

Dr. Harmanpreet Singh Kapoor

    Learning Objectives

• Introduction.
• Graphical presentation of frequency distribution
• Stem and Leaf Plot
• Suggested Readings

    1.    Learning Objectives

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

2.     Introduction

In this module, one can get a depth knowledge of different types of diagram like pie chart and graphical representations of the data like histogram, frequency polygon etc. This module is continuation of the previous module. Hence it is desired that reader must go through the previous module before further reading. We have already discussed about the frequency distribution and its different forms in the previous module. In this module, graphical representation of the frequency distribution and its types will be discussed. Other diagrammatic and graphical methods and their properties are also discussed. This module will help to develop an understanding of different methods of graphical and diagrammatic presentation of the data. In the following section, graphical presentation of frequency distributions are discussed in detail.

3.     Graphical presentation of frequency distribution

Graphs which consider the frequencies for the presentation of the data are called frequency graphs. These graphs are used to describe the characteristic feature of the frequency data. The methods for the preparation of the frequency table is already discussed in the previous module. The frequency graphs usually depends on the type of data whether it is discrete or continuous. Discrete data are usually represented in the form of bar diagrams or discontinuous curves while the continuous data are represented by means of curves.

While constructing the frequency graphs, usually the value of the variables are taken on the x-axis and the corresponding frequencies are represented on y-axis. The graphs that are used for this purpose are:-

(i)    Histogram

(ii)   Frequency Polygon

(iii)  Ogives

(i) Histogram: It is among the most commonly used method for the diagrammatic representation of a grouped frequency distribution. On one axis it consists of bars with height proportional to class frequencies and the width of the bar is defined through the class boundaries presented on the horizontal scale. In general, same width is considered for all the bars but it is not essential as it depend on the class width. In histogram , there is difference in terms of height only due to the class frequencies. The area of each bar is calculated by multiplying the width of the class and the frequency.

Sometime people are confused about bar diagram and histogram. The main difference between the bar diagram and histogram is that there is no difference between the bars in histogram while in bar diagram there is a gap between the bars. Also the bars in the bar diagram are of equal width but in histogram it depends on the width of classes and may be unequal due to unequal class width. Also it should be remember that histogram can only be constructed for open ended class width if magnitude of first open class is same as next class and the magnitude of the last class is same as preceding class.

The following example helps to get an idea about the construction of the histogram. The data is given in the following table:

From the above figure, one can observe that class marks are shown on the x-axis and the corresponding frequency is available on y-axis. The height of the bar is based on the frequency value. Also from the Figure 1, one can notice that there is no gap between the bars because values in the tables are shown in intervals and there is no gap in the upper limit of one class and the lower limit of the succeeding class. So to represent the continuous data in an exact manner bars are represented in the figure without any gap. On the other hand bar diagram is basically used to show the frequency of individual observations. Hence there is gap in the bars due to difference between the observations to maintain the difference. This is the major difference between histogram and the bar diagram. The following example will help to understand the differences between the two in detail.

From the above bar diagram, one can observe that there is gap in the bars that justify our discussion on histogram and bar diagram.

Hence, one can understand the difference between histogram and bar chart by keeping in mind the above examples.

Now as we are familiar with histogram, another most commonly used method for the graphical presentation of the data is frequency polygon.

(ii) Frequency Polygon: Frequency Polygon is considered as another method, other then histogram for graphical representation of the data. It is generally plotted when all the classes have same width. It is obtained by joining the mid value of the class interval corresponding to the class frequency. The end points of the polygon are joined to the x-axis that is basically the mid-point of classes at end of the frequency distribution. Hence frequency polygon is used in the situation of same class width and covered similar area as histogram.

Frequency polygon helps in understanding the skewness property of the data. One can detect the mode value from frequency polygon by drawing a perpendicular from the highest point on the curve to the x-axis. The frequency polygon of various distributions can be plotted on the same axis for comparison purpose but this is not possible in the case of histogram. In Histogram, if we have to compare two histogram of different data sets then we require two separate graphs. Also frequency polygon is a continuous curve and it has other benefits like determination of the slope, rough estimates of a particular value on the x-axis, at what rate observations are changing. Another important feature of the frequency polygon is that it can be drawn without plotting the histogram only when the mid-points of the classes are known.

In the following graph shown in Figure 3, a frequency polygon is constructed from Table 1 data. In the graph, one can observe that it is a curve that is represented with the joining of mid points of class interval and corresponding class frequency on the y-axis.

Frequency Curve

Frequency curve is the term that is basically used for the presentation of the probability distribution of continuous variable. As continuous variable takes values in small interval and the range of these variables approaches to infinite. So if we decrease the width of class intervals and at the same time increase the total frequency of the data that approaches to infinite then the shape of the histogram and the frequency polygon is approximate close to the shape of the frequency curve. In that case, the horizontal axis will represent the range of the variable and the vertical axis will show the frequency of a values in an interval. If it is feasible to present the relative frequency of the dataset on the vertical axis then it shows the percentage of particular class interval. This method of representing the data will help you to understand the concept of probability distribution function in future where we have probability values on the vertical axis that is derived from a mathematical function. On the other hand, the range of continuous variable is shown on horizontal axis. As the variable is continuous so the probability of a particular point is zero. So probability are evaluated in terms of intervals. So one can correlate the

probability distribution curve and the frequency curve from the concept. The topic of probability distribution function will be discussed in the further modules.

As we already discussed about the frequency curve, there are basically five types of frequency curves in the literature. These are (a) Symmetrical bell shaped (b) Uniform (c) U-shaped (d) J shaped and (e) asymmetric (Positive or negative skew)

(a) Symmetrical bell shaped: In this type of curve, the class frequency values keep on increasing steadily and after attaining a maximum value it keep on decreasing in the same pace as while increasing. It can be checked whether the curve is symmetric if we fold the curve from the centre then the two half the frequency curve must coincide. This is the reason that such type of curve is called symmetrical curve that has same area under curve on both side of the middle part or centre value. Another feature of symmetric curve is that it has single peakness at the middle and lessen slowly on both end.

Link for resource

http://slideplayer.com/slide/4929425/

(b) Uniform Curve: This type of curve will only occur if all the observations have same frequency. So it means when occurrence of each observation in the dataset is same then such type of curve appear. For example, in Figure 4 (b) figure represent the score of students of class. If these is a great possibility that all students score equal marks in the class test or examination. In such the uniform frequency curve will appear.

(c) U-Shaped: In this type of frequency curve, the highest value of the frequency occurs at the end or extreme point and the frequency keep on decreasing as the till the central part of the data and keep on increasing at the same pace of decreasing before reaching the middle part. This curve is just the opposite of the symmetric curve in shape. In this curve the most of the values occur at the extreme point and the less values come from intermediate point.

(d) J-Shaped: In this curve, the value of the variable attains the maximum frequency at one of its extreme points only. Hence it is different from U-shaped curve where maximum value attained at both extreme values. In a J-shaped curve, the values has less frequency in the lower class interval and then frequency keep on increasing steadily as the value of variable increases. Hence at the extreme point the distribution attains its maximum value.

(e) Asymmetric: This type of frequency curve has the highest frequency not in the central part of the data but on the either side of the central value. If the curve has longer tail toward the right side then the distribution is said to be positively skewed. If the curve has longer tail towards the left side then the distribution is said to be negative skewed.

(iii) Ogive: Ogive curve is constructed from the cumulative values of frequency i.e. cumulative frequency values are plotted against the x-axis. There are two types of ogive curves less than or more than. Less than ogive curve begin from the first interval and keep on increasing upwards corresponding to the next interval as the frequency are cumulated that means frequency values of previous frequency are added in next frequency values. Hence it keeps on increasing and at the last interval it shows the total frequency of data plotted against the last interval. Similarly, more than ogive curve begin from the total cumulative value from the first interval and keep on decreasing at next interval by subtracting the previous interval frequency from the total frequency value. If we repeat this process till the last interval then one can observe that the curve seem to be like a elongated S and is sometimes calls a double curve with one portion being concave and the other being convex. Also ogive curve can be constructed for unequal width of classes in the frequency distribution.

It is also possible to construct more than or less than ogive curve on the same graph and one can observe that if both curve are drawn on the same graph, these curve intersect at a point. X-axis value of that point is the median value of the frequency distribution. Hence ogive curve will help to get an idea about characteristics of the data as it is only the diagrammatic representation of the cumulative frequency distribution. There are some of the uses of the ogive which are as follows:

(a) Ogive curve is used to find out the median of the frequency distribution. It is also used to find out quartiles, deciles and percentiles etc.

(b) It is used to observe the cumulative frequency of a particular class interval of more than and less than type.

(c) From the shape of the curve one can observe the number of observations which are expected to lie between two given values.

It should be noted that it may be possible that one may not be able to estimate the correct value from the ogive curve. Hence, one should be careful while using ogives.

An example will help to understand the concept in depth. The cumulative frequency distribution (less than type) of data used in previous examples are shown below:

In Figure 5, ogive curve represents the cumulative frequency of less than type and it is of increasing type. We use the same data for graphical representation of the more than type of ogive type to see the difference of two type of ogive curve.

In Figure 7, ogive curve of two types are plotted graphically. From intersection point of these curve draw a perpendicular to the cumulative frequency polygon, horizontal scale i.e. these two curves intersect at point value 49 at y-axis and approx. 30 at x-axis. This approximate value is considered as the median value of the data. In the next section, we will discuss Stem and leaf display that is considered as another method for the.representation of the data.

4. Stem and Leaf plot

It is considered as an alternative to the histogram. Although it gives a visual representation similar to the histogram but it does not lose the details of the individual data points in the grouping. For example, the data of expenditure on calls in a week of 30 persons are given below:

11,22,22,25,27,28,29,34,35,36,37,37,38,39,39,39,43,46,49,49,49,49,52,56,58,64,65,74,82,91

The stems on the left represent the 10 units and the leaves on the right represent the units of ones. So the individual data points can be represented in the diagram. From the diagram, one can observe that it seems like a histogram but the difference here is that the values are used in place of bars. Hence the major drawback of this diagram is that when we have large amount of then it is difficult to make stem and leaf diagram.

In the next section, we will discuss about the diagrammatical representation of the data through the pie chart.

5. Pie-Chart

When the total values can be represented by a big circle and the various components by sectors cut inside it. This type of diagram is known as pie diagram and it is also used to show the percentage breakdown. The total is represented by 360 degree angle. It can be divided into a number of small angles whose degree is according to the values of the categories in the data. There are some steps for the construction of pie diagram. These are

(a) The category or items values are expressed either in percentage or degree. For example, number of males/females in the data are expressed either in percentage or in degrees.

(b) One can find the percentage of the items by dividing its value by the aggregate one and multiple each of them by 3.6.

Hence one can find two forms of pie chart, one is in percentage form and other in degree term.

For example, the following data represent the expenditure on entertainment and communication of household

Hence one can easily understand the expenditure on items through percentages from the pie diagram. This is the reason that pie chart is mostly used to present the data as it is easily understandable even by a layman.

In the real world large type of diagrammatic methods are used for the presentation of the statistical data. Some of the types are like one- dimensional diagram, two-dimensional diagram, three-dimensional diagram and pictogram etc. In this module, we discussed some of its types like histogram, bar diagram, frequency polygon, frequency curve, ogives and pie charts. Differences between histogram and bar diagram are discussed. Importance of all these graphical and diagrammatical representation is discussed with examples. Frequency curve and its different types are also discussed. These diagrams and graphical representations are useful as they present the data in an 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 can understand this without any previous knowledge of statistics. This is the reason that diagrams, pictures and graphs are used to give primary education to the kids.

7. 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.

• Diagrammatic representation
• Geometric principles
• One-dimensional diagram
• Two-dimensional diagram
• Three-dimensional diagram

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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

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Maity, S.K. (2021). Diagrammatic Representation of Geographical Data. In: Essential Graphical Techniques in Geography. Advances in Geographical and Environmental Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-16-6585-1_3

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