(Q4) If the median of 60 observations, given below is 28.5, find the values of x and y.

Class Interval 0-10 10-20 20-30 30-40 40-50 50-60
Frequency 5 x 20 15 y 5

Answer :

Class Interval Frequency c.f.
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
Median = l +
(
n
2
 - cf )
f
 × h

It is given that ∑f = n =

So, 45 + x + y =

x + y = - 45 =

x + y = ....(1)

The median is 28.5 which lies be-tween 20 and 30.

Median class = 20-30

Lower boundary of the median class 'l' = 20

N
2
 =
2
 =

cf - cumulative frequency = 5 + x

h = 10

Median = l +
(
n
2
 - cf )
f
 × h
28.5 = +
- 5 - x
 ×
- x
 = 28.5 - =

- x = ×

x = - =

also from (1); x + y =

+ y =

y =

∴ x = ; y = .