Find the missing frequencies in the following distribution, if the sum of the frequencies is 120 and the mean is 50.

Class:	0-20	20-40	40-60	60-80	80-100
Frequency:	17	$f_1$	31	$f_2$	19.

Given:

The sum of the frequencies is 120 and the mean is 50.

To do:

We have to find the missing frequencies.

Solution:

Let the assumed mean be $A=50$.

Class size $h=20$

$\sum{f_i}=68+f_1+f_2$

$\Rightarrow 120=68+f_1+f_2$

$\Rightarrow 120-68=f_1+f_2$

$\Rightarrow f_1=52-f_2$..........(i)

Mean $=A+h \times \frac{\sum{f_iu_i}}{\sum{f_i}}$    

Therefore,  

Mean $50=50+20\times(\frac{4+f_2-f_1}{68+f_1+f_2})$

$50-50=20\times\frac{4+f_2-f_1}{68+f_1+f_2}$

$\frac{4+f_2-f_1}{68+f_1+f_2}=0$

$4+f_2-(52-f_2)=0$                     [From (i)]

$2f_2=48$

$f_2=24$

$\Rightarrow f_1=52-24=28$

The missing frequencies $f_1$ and $f_2$ are 28 and 24 respectively. 

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Updated on: 10-Oct-2022

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