An incomplete distribution is given below:

Variable:	10-20	20-30	30-40	40-50	50-60	60-70	70-800
Frequency:	12	30	-	65	-	25	18

You are given that the median value is 46 and the total number of items is 230.Using the median formula fill up missing frequencies.

Given:

An incomplete distribution is given. The median value is 46 and the total number of items is 230.

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 $= 46$ and $N = 230$

$150 + p_1 + p_2 = 230$

$p_1+p_2 = 230 - 150 = 80$

$p_2 = 80-p_1$.....….(i)

Median $= 46$ which lies in the class 40-50

$l = 40, f= 65, F = 42+p_1$ and $h = 50-40=10$

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

$46=40+\frac{\frac{230}{2}-(42+p_1)}{65}\times 10$

$46-40=\frac{115-42-p_1}{13}\times2$

$6(13)=(73-p_1)2$

$39=73-p_1$

$p_1=73-39=34$

$p_2 = 80 - 34 = 46$            [From (i)]

The missing frequencies are 34 and 46.

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Updated on: 10-Oct-2022

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