If the median of the following frequency distribution is 28.5 find the missing frequencies:

Class interval:	0-10	10-20	20-30	30-40	40-50	50-60	Total
Frequency:	5	$f_1$	20	15	$f_2$	5	60

Given:

The median of the given frequency distribution is 28.5.

To do:

We have to find the missing frequencies.

Solution:

Median $= 28.5$ and $N = 60$

$45 + f_1 + f_2 = 60$

$f_1+f_2 = 60 - 45 = 15$

$f_2 = 15-f_1$.....….(i)

Median $= 28.5$ which lies in the class 20-30

$l = 20, f= 20, F = 5+f_1$ and $h = 30-20=10$

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

Therefore,

$28.5=20+\frac{\frac{60}{2}-(5+f_1)}{20}\times 10$

$28.5-20=\frac{30-5-f_1}{2}$

$(8.5)2=25-f_1$

$17=25-f_1$

$f_1=25-17=8$

$f_2 = 15 - 8 = 7$            [From (i)]

The missing frequencies $f_1$ and $f_2$ are 8 and 7 respectively.

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Updated on: 10-Oct-2022

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