Question

An incomplete distribution is given as follows:

Variable:	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70
Frequency:	10	20	?	40	?	25	15

You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

Answer 1

Class interval	Frequency	Cumulative frequency
0 - 10	10	10
10 - 20	20	30
20 - 30	f1	30 + f1
30 - 40	40	70 + f1
40 - 50	f2	70 + f1 + f2
50 - 60	25	95 + f1 + f2
60 - 70	15	110 + f1 + f2
	N = 170

Given median = 35

The median class = 30 - 40

l = 30, h = 40 - 30 = 10, f = 40, F = 30 + f1

Median `=l+{(N/2-F)/f}xxh`

`35=30+{(85-(30 + f1))/40}xx10`

`35=30+(55-f1)/40xx10`

`35-30=(55-f1)/4`

`5=(55-f1)/4`

5 x 4 = 55 - f1

20 = 55 - f1

f1 = 55 - 20

f1 = 35

Given

Sum of frequencies = 170

⇒ 10 + 20 + f1 + 40 + f2 + 25+ 15 = 170

⇒ 10 + 20 + 35 + 40 + f2 + 25+ 15 = 170

⇒ 145 + f2 = 170

⇒ f2 = 170 - 145

⇒ f2 = 25

∴ f1 = 35 and f2 = 25