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Graphical Representation of data is a visually appealing representation of data done in statistics in the form of graphs, charts, lines, and plots. It is the method of comparison and analysis of qualitative and categorical data using discrete and non-discrete variables. They are simple and easily understandable. However, they lack complete accuracy of facts and cannot convey the exact information as provided by raw data. Bar graphs are the pictorial representation of categorical data in the form of rectangular bars of uniform width while histograms are graphical representations of solid bars with uniform width as well as varying width. A frequency polygon is the visual representation of quantitative data and its frequencies in the form of a polygon.
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Key Terms: Graphical Representation of Data, Statistics, Bar Graphs, Histograms, Frequency Polygons, Frequency Table, Class Intervals
Graphical Representation of Data: Types
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Methods or structures used to represent a given data graphically are of various forms. Some of the different types of graphical representations are:
- Line Graph: Also known as linear graphs. It helps represent the data on the changes of an event over time and is displayed in a continuous form using line segments.
- Bar Graph: It helps in the pictorial representation of categorical data in the form of rectangular bars (as heights or lengths) of uniform width and compares and analyses them using it. The categorical data used here is displayed as categorized with equal spacing between each solid bar and they do not touch each other.
- Histograms: Similar to the representation of a bar graph, it is represented using solid bars with uniform width as well as varying width. Histograms help in the distribution of grouped frequency of quantitative data with continuous class intervals.
- Pie Chart: Also known as circle graphs. It helps represent quantitative data and visualize them in the form of circles and then analyze it. The data used is displayed as parts of a whole.
- Line Plot: It is a graphical representation that helps represent a given data on a number line. Here, data points, called markers, are marked above a preferred number line.
- Frequency Polygon: They are the visual representation of quantitative data and its frequencies in the form of a polygon. They can be plotted with or without the help of histograms. The independent method of plotting a frequency polygon is done using the midpoints of the class intervals, called the class-marks.
- Frequency Table: It helps represent the frequency of certain data in a given class interval or group. The data provided are listed in ascending or descending order along with the number of occurrences a certain event happens to have.
Graphical Representation of Data: Principle
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Principles of graphical representation of data are algebraic and are applicable for all types of it. In every graph, a certain data point is displayed using variables representing coordinate axes of coordinate plane.
Coordinate axes are of two types, horizontal axes, and vertical axes, and are placed perpendicular to each other with both intersecting at the origin. The horizontal coordinate axis is known as X-axis while the vertical coordinate axis is known as the Y-axis.
Certain principles regarding graphical representation of data are as follows:
- On a coordinate plane, any point above the horizontal axis is taken as a positive value while any point below the horizontal is taken as a negative value.
- On a coordinate plane, any point to the right of the vertical axis is taken as a positive value while any point to the left of the vertical axis is taken as a negative value.
Bar Graphs
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Bar graphs help in pictorial representation of categorical data in the form of rectangular bars (as heights or lengths) of uniform width and compare it. The length proportional of the bar depicts the discrete data of the group or interval. The categorical data used here is displayed with equal spacing between each solid bar on the axis it is placed such that the bars do not touch each other.
Figure: Bar graphs
Bar graphs are constructed using the two coordinate axes and can be plotted horizontally or vertically. In such cases, one axis represents the type of group or intervals of the data categorized while the other axis represents the numerical or discrete value of the data provided. The most common form of plotting of bar graphs is done vertically and the bars are placed on the X-axis with equal spacing.
Simple bar graphs, sub-divided bar graphs, multiple bar graphs, and deviation bar graphs are some different types of bar graphs normally used in the construction of data graphically.
Histograms
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Histograms are a type of time series graph, constructed similar to that of a bar graph, represented using rectangular solid bars with uniform width as well as varying width. They were first introduced in 1891 by Karl Pearson.
Figure: Histograms
Histograms help in the frequency distribution of the quantitative data with continuous class intervals, where the height proportional of the bar depicts the frequency or percentage of the specific category and the width proportional of the bar depicts the width or class intervals of the category. The rectangular solid bars used in the graphical representation of the data are displayed in continuous form.
Frequency Polygons
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Frequency polygons are the visual representation of quantitative data and its frequencies in the form of a polygon. They can be plotted with or without the help of histograms. The independent method of plotting a frequency polygon is done without constructing histograms.
Figure: Frequency polygon
To independently plot a frequency polygon, one has to find the class-marks, that is, the midpoints of the class intervals used in the data.
The class-mark of a given data can be calculated by dividing the sum of the upper limit and lower limit of a class by 2. The formula for calculating the class-mark is as follows:
Class-mark=Upper Limit + Lower Limit2
Things to Remember
- Graphical Representation of the data is a visual representation of data in statistics done in the form of graphs, charts, lines, and plots. This method is used for the comparison and analysis of qualitative and categorical data using discrete and non-discrete variables.
- While plotting a graph, make sure that it has a proper title, scale, unit of measurement, index, and data sources. It should be neat, simple, and easy to understand.
- Graphical representations are used in finding the mean, median, and mode of different data provided. They are also used in determining the interpolation and extrapolation of the given data.
- They are simple, easily understandable, and appealing to the eye.
- There is no equal spacing between each solid bar and they touch each other.
Sample Questions
Ques. Mention any four types of graphical representation of the data. (4 Marks)
Ans. Some of the different types of graphical representation of the data are as follows:
- Bar Graph: It helps in the pictorial representation of categorical data in the form of rectangular bars (as heights or lengths) of uniform width and compares and analyses them using it. The categorical data used here is displayed as categorized with equal spacing between each solid bar and they do not touch each other.
- Histograms: Similar to the representation of a bar graph, it is represented using solid bars with uniform width as well as varying width. Histograms help in the distribution of grouped frequency of quantitative data with continuous class intervals.
- Frequency Polygon: They are the visual representation of quantitative data and its frequencies in the form of a polygon. They can be plotted with or without the help of histograms. The independent method of plotting a frequency polygon is done using the midpoints of the class intervals, called the class-marks.
- Pie Chart: Also known as circle graphs. It helps represent quantitative data and visualize them in the form of circles and then analyze it. The data used is displayed as parts of a whole.
Ques. What are the limitations of using a graph? (3 Marks)
Ans. The graphical representation of data has the following limitations:
- Only selected characteristics of data are displayed in a graphical representation.
- It lacks the complete accuracy of the facts used or the data provided.
- Interpretation and analysis of a given graph cannot be done by a layman nor can they understand it.
- The graph portrays the arbitrary tendencies of the data only and one cannot understand the actual values used just by looking at it.
- It can only be used to represent numerical data and not statements.
Ques. Differentiate between a bar graph and a histogram. (3 Marks)
Ans. A bar graph and a histogram are differentiated as follows:
| Bar Graph | Histogram |
| Bar graphs help in the pictorial representation of categorical data in the form of rectangular bars (as heights or lengths) and compare it. | Histograms help in the frequency distribution of the quantitative data with continuous class intervals. |
| The data provided is represented pictorially. | The data provided is represented graphically |
| Discrete variables are distributed | Non-discrete variables are distributed. |
| Equal spacing between each solid bar and they do not touch each other. | No equal spacing between each solid bar and they touch each other. |
| The data used is categorical | The data used is quantitative |
| Have uniform width | May have uniform width or varying width |
Ques. In a particular section of Class IX, 40 students were asked about their birth month and the following graph was prepared for the data obtained. (3 Marks)
Answer the following questions after observing the graph given above.
How many students were born in the month of November?
In which month was the maximum number of students born.
Ans. In the given bar graph, the variable plotted on the X-axis is the ‘Months of Birth’ and the value of the variable plotted on the Y-axis is the ‘Number of Students’.
- By observing the graph, one can find that the number of students born in November is 4.
- By observing the graph, one can find that the maximum number of students were born in August.
Ques. The weekly observations made in a study on the cost of living index in a city is given as follows:
| Cost of Living Index | Number of Weeks |
| 150-160 | 10 |
| 160-170 | 20 |
| 170-180 | 9 |
| 180-190 | 6 |
| 190-200 | 2 |
| Total | 47 |
Calculate the class-mark of the given data and form a new table displaying it. (5 Marks)
Ans. The formula used to calculate class-mark is given by, Class-mark=Upper Limit + Lower Limit2
For the class 150-160, the Upper Limit = 160 and the Lower Limit = 150
So, the Class-mark=160+1502=155
For the class 160-170, the Upper Limit = 170 and the Lower Limit = 160
So, the Class-mark=170+1602=165
For the class 170-180, the Upper Limit = 180 and the Lower Limit = 170
So, the Class-mark=180+1702=175
For the class 180-190, the Upper Limit = 190 and the Lower Limit = 180
So, the Class-mark=190+1802=185
For the class 190-200, the Upper Limit = 200 and the Lower Limit = 190
So, the Class-mark=200+1902=195
Hence, the new table with the class-mark is formed as follows:
| Cost of Living Index | Class-mark | Number of Weeks |
| 150-160 | 155 | 10 |
| 160-170 | 165 | 20 |
| 170-180 | 175 | 9 |
| 180-190 | 185 | 6 |
| 190-200 | 195 | 2 |
| Total | 47 | |
Ques. What are the advantages of representing data graphically? (4 Marks)
Ans. The graphical representation of data has the following advantages:
- The graphical representation of data in statistics helps in finding the mean, median, and mode of different data provided.
- Graphs help in the interpolation and extrapolation of a given data.
- Graphical representation helps in comparing and analyzing the given data for different periods of time or intervals.
- It saves a lot of time as a graphical representation is much simpler to study than raw data.
- No prior knowledge is required in interpreting a given data using a graph as it is easily understandable.
Ques. What are frequency polygons? How is class-mark calculated? (3 Marks)
Ans. Frequency polygons are the visual representation of quantitative data and its frequencies in the form of a polygon. They can be plotted with the help of histograms or independently using the class-mark.
Class-marks are the midpoints of the class intervals used in the data and can be calculated by dividing the sum of the upper limit and lower limit of a class by 2. The formula for calculating the class-mark is as follows:
Class-mark=Upper Limit + Lower Limit2
Ques. Mention any four rules of graphical representation of the data. (3 Marks)
Ans. The rules of graphical representation of the data are as follows:
- A proper heading or title is a must while representing a given data graphically to convey the real subject behind it.
- It is necessary to mention the unit of measurement used while plotting the graph.
- A suitable scale used to plot the given data graphically must be properly mentioned for each variable and it ensures the accuracy of the graph.
- The source of data or information (data sources) used while representing the data graphically should be displayed at the bottom of the graph constructed to convey its authenticity.
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