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 frequencies is 170. Using the median formula, fill up the missing frequencies.

Given:

An incomplete distribution is given. The median value is 35 and the sum of all frequencies is 170.

To do:

We have to find the missing frequencies using the median formula.

Solution:

Let $p_1$ and $p_2$ be the missing frequencies.

Median $= 35$ and $N = 170$

$110 + p_1 + p_2 = 170$

$p_1+p_2 = 170 - 110 = 60$

$p_2 = 60-p_1$.....….(i)

Median $= 35$ which lies in the class 30-40

$l = 30, f= 40, F = 30+p_1$ and $h = 40-30=10$

Median $=l+(\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{f}) \times h$

$35=30+\frac{\frac{170}{2}-(30+p_1)}{40}\times 10$

$35-30=\frac{85-30-p_1}{4}$

$4(5)=55-p_1$

$p_1=55-20$

$p_1=35$

$p_2 = 60 - 35 = 25$            [From (i)]

The missing frequencies are 35 and 25.

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Updated on: 10-Oct-2022

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