Question

If the median of the distribution given below is 28.5, find the values of x and y.Class interval	Frequency
0 - 10	5
10 - 20	x
20 - 30	20
30 - 40	15
40 - 50	y
50 - 60	5
Total	60

Answer 1

The cumulative frequency for the given data is calculated as follows.

Class interval	Frequency	Cumulative frequency
0 - 10	5	5
10 - 20	x	5 + x
20 - 30	20	25 + x
30 - 40	15	40 + x
40 - 50	y	40 + x +y
50 - 60	5	45 + x +y
Total	60

From the table, it can be observed that n = 60

45 + x + y = 60 or x + y = 15 ……………………….(1)
Median of the data is given as 28.5 which lies in interval 20 − 30.

Therefore, median class = 20 − 30
Lower limit ($l$) of median class = 20
Cumulative frequency ($cf$) of class preceding the median class = 5 + x
Frequency ($f$) of median class = 20
Class size ($h$) = 10

Median = $l + (\frac{\frac{n}2 - cf}{f})\times h$

28.5 = $20 + [\frac{\frac{60}2 - (5 +x)}{20}]\times 10$

8.5 = $(\frac{25 - x}2)$

17 = 25 - x
x = 8

From equation (1),
8 + y = 15
y = 7

Hence, the values of x and y are 8 and 7 respectively.