An incomplete distribution is given as follows: Variable: 0 - 10, 20 - 30, 20 - 30, 40 - 50, 50 - 60, 60 - 70

Question

An incomplete distribution is given as follows:

Variable:	0 - 10	20 - 30	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 frequency.

Answer 1

Class interval	Frequency	Cumulative frequency
0 - 10	10	10
10 - 20	20	30
20 - 30	f1	30 + f1 (F)
30 - 40	40 (f)	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 = 10, f = 40 and F = 30 + f₁

Median = l + \(\frac{\frac{N}{2}-F}{f}\)

\(30=30+\frac{85-(30+f_1)}{40}\times 10\)

\(5=\frac{55-f_1}{4}\)

f₁ = 55 – 20 = 35

Given, 

Sum of frequencies = 170

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

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

= f₂ = 170 – 145 = 25

Therefore, 

f₁ = 35 and f₂ = 25