If the median of the distribution given below is 28.5, find the values of x and y.

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

From the table, it can be observed that n = 60
45 + x + y = 60 or x + y = 15 …(1)
Median of thr 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 + ((n/2 – cf)/(f)) × h
⇒ 28.5 = 20 + {(60/2 – (5 + x))/20} × 10
⇒ 8.5 = (25 – x)/2
⇒ 17 = 25 – x
⇒ x = 8
From equation (1), 8 + y = 15 ⇒ y = 7
Hence, the value of x and y are 8 and 7 respectively.