ICSE Class 8 Maths Chapter 35 Graphical Represention of Statistical Data

Chapter 35: Graphical Representation Of Statistical Data

Review

As compared to written statement, the graphical representation of statistical data has a more lasting effect on the mind. Of course, a graphical representation should be properly titled and labelled so as to convey what it is about.

Out of various types of graphical representations, the followings are discussed in this chapter:

1. Bar graph or Bar chart 2. Pie graph or Pie chart 3. Histogram

Bar Graph (Bar Chart)

It is the simplest and the most widely used graph, in which the numerical data is represented by the height of rectangular bars of equal width.

Example 1

The approximate speeds of some objects are given below. Draw a bar graph to represent them.

Solution

The required bar graph is as given alongside:

Steps

1. Take the names of objects along X-axis and velocities along Y-axis.

2. All the bars drawn should be of the same width.

3. Same spaces should be left between the consecutive bars.

Pie Graph (or Pie Chart)

When the numerical data is represented by the sectors of a circle, the graph obtained is called a pie graph or pie chart.

An angle, whose vertex is the centre of a circle, is called central angle and the region of the circle enclosed by the arms of the angle is called sector.

In the adjoining figure, angle AOB is the central angle and shaded portion of the circle is the sector.

Example 2

Use the information given in example 1, to draw a pie-graph.

Solution

Steps

1. Since the angle about the centre of circle is 360 degrees, divide 360 degrees in proportion of given data. In this example, divide 360 degrees in proportion 10 : 40 : 60 : 50 : 80 to obtain the corresponding central angle.

2. Make a table as given below.

3. Draw a circle of any suitable radius.

4. For each central-angle, draw a sector.

Histogram

Histogram is a graphical representation of grouped frequency distributions. In this case, the bars (rectangles) are drawn with class-intervals as bases along X-axis and their heights along Y-axis, proportional to the frequencies of respective classes.

Example 3

In a class of 40 students, the marks obtained (out of 50) are as given below:

Draw a histogram to represent the given data.

Solution

Steps

1. Taking suitable scales, mark the class-intervals (marks) on the X-axis and frequency (the no. of students) on Y-axis.

2. Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.

Example 4

Draw a histogram to represent the following data:

Solution

Since, the lower limit of first class-interval is 50; therefore, the scale on X-axis starts at 50.

To reduce the size of the graph, leave some suitable space between the origin and marking of 50 on X-axis, and draw a zig-zag line in this space.

The zig-zag line between the origin and the first marking (50 in this example) shows that the graph is drawn to scale beginning at 50, and not at the origin itself.

Teacher's Note

Bar graphs and pie charts are commonly used in news reports and business presentations to make data easy to understand at a glance. Understanding how to read these visual representations helps us make informed decisions about everything from budgets to product choices.

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