Question

Draw 'less than ogive' and 'more than ogive' on a single graph paper and hence find the median of the following data:

Class interval	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	12	2	4	3	4	3

Answer 1

The frequency distribution table of less than type is as follows:

Class interval (upper class limits)	Cumulative frequency (cf)
Less than 10	2
Less than 15	2 + 12 = 14
Less than 20	14 + 2 = 16
Less than 25	16 + 4 = 20
Less than 30	20 + 3 = 23
Less than 35	23 + 4 = 27
Less than 40	27 + 3 = 30

and the frequency distribution table of more than type is as follows:

Class interval (lower class limits)	Cumulative frequency (cf)
More than 5	28 + 2 = 30
More than 10	16 + 12 = 28
More than 15	14 + 2 = 16
More than 20	10 + 4 = 14
More than 25	7 + 3 = 10
More than 30	3 + 4 = 7
More than 35	3

Taking upper class limits and lower class limits of class intervals on x−axis and their respective frequencies on y−axis, its ogive can be drawn as follows:

​

Here both ogives intersect at point A whose x−coordinate is 17.5.



Thus, the median of the data is 17.5.