Question

If the median of the distribution is 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 (n)	60

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

45 + x + y = 60

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

From equation (1),

8 + y = 15

y = 7

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