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 (n)	60

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

45 + x + y = 60

x + y = 15 (1)

the median of the data is given as 28.5, which lies in the intervals 20 − 30.

Therefore, the median class is 20 − 30

lower limit (l) of the median class is 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)xxh`

`28.5 = 20 + [(60/2-(5+x))/20]xx10`

`8.5 = ((25-x)/2)`

17 = 25 − x

8 + y =  15

y = 7

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