Question

The median of the following data is 32.5, find the missing frequencies x and y:

Class:	0 – 10	10 – 20	20 – 30	30 – 40	40 –50	50 – 60	60 – 70	Total
Frequency:	x	5	9	12	y	3	2	40

Answer 1

Total frequency Σf = 40.

x + 5 + 9 + 12 + y + 3 + 2 = 40

⇒ x + y + 31 = 40

⇒ x + y = 9   ...(Equation 1)

Median is 32.5, which falls in class 30 – 40.

Median Formula: `M = l + ((N//2 - cf)/f) xx h`.

Here, l = 30, N/2 = 20, f = 12, h = 10.

Cumulative frequency before median class (cf) = x + 5 + 9 = x + 14.

`32.5 = 30 + ((20 - (x + 14))/12) xx 10`

`2.5 = ((6 - x)/12) xx 10`

`2.5 xx 12/10 = 6 - x`

⇒ 3 = 6 – x

⇒ x = 3

Substitute x = 3 into equation (1):

3 + y = 9

⇒ y = 6

The missing frequencies are x = 3 and y = 6.