ICSE Class 8 Maths Statistics Chapter 35 Diagrammatic Representation of Data

Diagrammatic Representation Of Data

Column Graphs/Bar Charts

Pie Charts

Histograms

Choosing a Diagrammatic Representation

Introduction

We have seen data being represented by various graphical or diagrammatic forms since primary school. Beginning with pictographs we saw data displayed in column graphs, bar charts, pie charts, and line graphs. We have learnt how to interpret information from such representations as well as how to construct them, given the relevant data. Having learnt about frequency distributions, let us now construct column graphs, pie charts, and histograms, given a frequency distribution.

Column Graphs/Bar Charts

The method of construction for column graphs and bar charts is the same, drawing rectangles whose lengths correspond to the frequency of observations. However, in column graphs, the rectangles are tall and interpretations are made by comparing the heights of columns. In bar charts, the rectangles are horizontally extended to the extent of their frequencies and interpretations are made by comparing the lengths of the bars.

Each column or bar is of equal width and the space between the columns or bars is equal.

Example 1

This simple frequency distribution shows the number of students in a particular class who wear a certain shoe size.

Construct a column graph to display the given information.

The observations are placed at equal distance to each other on the X axis while the frequencies are displayed with rectangles whose heights can be measured off on the Y axis.

Teacher's Note

When shopping for clothes or shoes, you might notice store owners using column graphs to track which sizes sell the most, helping them decide how much inventory to stock.

Example 2

The attendance recorded in a swimming pool during a swimming season is given in the table below. Construct a bar chart to display the given information.

The bar chart is required to display the data in two simple frequency distributions. The sets of frequencies that represent boys and girls are shown by bars shaded differently.

Note that:

1. The months are placed on the Y axis.

2. The length of the bars correspond to the frequencies represented on the X axis.

3. A scale of 100 children = 0.7 cm has been selected for convenience of display.

4. The broken line on the X axis represents frequencies less than 1500 that have not been displayed, as they are below the range of the data.

Teacher's Note

Schools often use bar charts to track attendance patterns across different months to identify trends and plan special events or activities accordingly.

Pie Charts

In pie charts a circular region is divided into as many sectors as there are observations or classes. The central angle of a sector subtended by its arc is proportional to the frequency. Pie charts may be used to display data from a simple as well as a grouped frequency distribution.

Example 3

Jayant received Rs 1800 as a gift and kept a record of how he spent every rupee.

Construct a pie chart to display how Jayant spent his money.

The total money spent will represent a complete angle or 360 in the pie chart. Each expense head will be represented by a sector. First, the central angle subtended by the arc of each sector is calculated as shown below:

Break-up of Rs 1800 spent by Jayant:

Teacher's Note

When your family discusses household budget allocation, pie charts help visualize what percentage of income goes toward food, utilities, entertainment, and savings in an easy-to-understand format.

Example 4

The grouped frequency distribution that follows, gives the age profile of audience in a cinema hall screening an animated film. Construct a pie chart to display the given information.

Find the magnitudes of the central angles of different classes.

Age profile of audience watching animated film:

Histograms

Grouped frequency distributions are generally represented diagrammatically by histograms.

The construction of histograms is similar to that of column graphs. The difference between the two is that instead of the rectangles being placed on the observations axis as in a column graph, in a histogram the rectangles are placed between the class limits that are represented along the X axis, thus leaving no space between the rectangles. This is why the class limits need to be true class limits in exclusive forms of class intervals.

Example 5

The marks obtained by 50 students in an examination are shown in the grouped frequency distribution below. Construct a histogram to display the given information.

Teacher's Note

Teachers use histograms when displaying student test scores to quickly identify how many students scored in different ranges, making it easier to plan remedial or advanced lessons.

Example 6

The income profile of 85 employees in a factory is shown in the grouped frequency distribution below. Construct a histogram to display the given information.

The class intervals in the income groups are in inclusive form. In order to construct a histogram, the class intervals need to be first converted into exclusive form.

15001 - 15000 = 1 and half of 1 = 0.5. Thus the new frequency distribution with continuous data will be as follows:

for its presentation or a grouped frequency distribution.

Similarly, the various forms of diagrammatic representation are suitable for different types of data.

Although pie charts can be constructed for a simple as well as a grouped frequency distribution, they are generally used for data in which there is variety in the frequency. As the viewer cannot be expected to measure each central angle of a sector with a protractor, only such classes, the frequencies of which are clearly comparable, are suitable to be shown in a pie chart.

The fine differences in frequencies which are not suitable to be shown in a pie chart can be shown in a column graph. As the difference in vertical heights of rectangles are distinct and clearly visible, this method of diagrammatic representation is preferred for display of simple frequency distributions.

Simple frequency distributions in which a trend is to be displayed diagrammatically are best represented by line graphs. The jagged rise and fall of the graph clearly shows the trend of fluctuating data like prices or temperatures.

Grouped frequency distributions are represented diagrammatically by histograms.

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