If the median of the following data is 32.5, find the missing frequencies.

Class interval:	0-10	10-20	20-30	30-40	40-50	50-60	60-70	Total
Frequency:	$f_1$	5	9	12	$f_2$	3	2	40

Given:

The median of the given data is 32.5.

To do:

We have to find the missing frequencies.

Solution:

Median $= 32.5$ and $N = 40$

$31 + f_1 + f_2 = 40$

$f_1+f_2 = 40 - 31 = 9$

$f_2 = 9-f_1$.....….(i)

Median $= 32.5$ which lies in the class 30-40

$l = 30, f= 12, F =14+f_1$ and $h = 40-30=10$

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

Therefore,

$32.5=30+\frac{\frac{40}{2}-(14+f_1)}{12}\times 10$

$32.5-30=\frac{20-14-f_1}{6}\times 5$

$(2.5)6=(6-f_1)5$

$15=30-5f_1$

$5f_1=30-15=15$

$f_1=\frac{15}{5}=3$

$f_2 = 9 - 3 = 6$            [From (i)]

The missing frequencies $f_1$ and $f_2$ are 3 and 6 respectively.

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Updated on: 10-Oct-2022

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