The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency $f_1$ and $f_2$.

Class:	0-20	20-40	40-60	60-80	80-100	100-120
Frequency:	5	$f_1$	10	$f_2$	7	8.

Given:

The mean of the given frequency distribution is 62.8 and the sum of all the frequencies is 50.

To do:

We have to compute the missing frequencies $f_1$ and $f_2$.

Solution:

Mean $=62.8$ and $\sum{f_i}=50$

This implies,

$30+f_1+f_2=50$

$\Rightarrow f_1+f_2=50-30$

$\Rightarrow f_1=20-f_2$...........(i)

 We know that,

Mean $=\frac{\sum{f_ix_i}}{\sum{f_i}}$    

Therefore,  

Mean $62.8=\frac{2060+30f_1+70f_2}{30+f_1+f_2}$

$62.8[30+(20-f_2)+f_2]=2060+30(20-f_2)+70f_2$                       [From (i)]

$1884+1256=2060+600-30f_2+70f_2$

$3140-2660=40f_2$

$f_2=\frac{480}{40}$

$f_2=12$

$\Rightarrow f_1=20-12=8$.

The missing frequencies $f_1$ and $f_2$ are $8$ and $12$ respectively.

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Updated on: 10-Oct-2022

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