To Draw the Graph of Frequency Polygon, We Need to Find Mid Points

Example:

Construct a Frequency polygon for the following frequency distribution relating to the ages of telephone operators.

Age (Years) / 15 – 19 / 20 – 24 / 25 – 29 / 30 – 34 / 35 – 39 / 40 – 44
No. of operators / 9 / 188 / 160 / 123 / 84 / 15

Solution:

To draw the graph of frequency polygon, we need to find mid points.

Class Limits / Class Boundaries / Frequency / Midpoints
15 – 19 / 14.5 – 19.5 / 9 / 17
20 – 24 / 19.5 – 24.5 / 188 / 22
25 – 29 / 24.5 – 29.5 / 160 / 27
30 – 34 / 29.5 – 34.5 / 123 / 32
35 – 39 / 34.5 – 39.5 / 84 / 37
40 – 44 / 39.5 – 44.5 / 15 / 42

Frequency Polygon:

This figure is not two sided closed figure. So, we need first and last values of midpoints as well as frequency.

Class Limits / Class Boundaries / Frequency / Midpoints
10 - 14 / 9.5 – 14.5 / 0 / 12
15 – 19 / 14.5 – 19.5 / 9 / 17
20 – 24 / 19.5 – 24.5 / 188 / 22
25 – 29 / 24.5 – 29.5 / 160 / 27
30 – 34 / 29.5 – 34.5 / 123 / 32
35 – 39 / 34.5 – 39.5 / 84 / 37
40 – 44 / 39.5 – 44.5 / 15 / 42
45 – 49 / 44.5 – 49.5 / 0 / 47

The first class of class boundaries will be getting by subtracting the class interval from the lower and upper limits. Similarly, the last class of class boundaries will be getting by adding the class interval from the lower and upper limits.