Question

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

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

Answer 1

Let A = 30, h = 20

Class	$x_i$	$f_i$	$u_i=\frac{x_i-A}{h}$	$f_i{u}_i$
0 - 20	10	5	-1	-5
20 - 40	30	$f_i$	0	0
40 - 60	50	10	+1	10
60 - 80	70	$f_2$	+2	$2f_2$
80 - 100	90	7	+3	21
100 - 120	110	8	+4	32
		$\sum f_i=30+f_1+f_2$		$\sum f_i{u}_i=58+2f_2$

Given $30+f_1+f_2=50\Rightarrow f_1+f_2=20$.........(i)
$\overline{x}=A+(\frac{\sum f_i{u}_i}{\sum f_i}\times h)\Rightarrow 62.8=30+(\frac{58+2f_2}{50}\times 20)$
$32.8=(58+2f_2)\times \frac{2}{5}\Rightarrow 32.8\times 5=116+4f_2\Rightarrow 164=116+4f_2$
$4f_2=164-116\Rightarrow 4f_2=48\Rightarrow f_2=12$
Now $f_1+f_2=20\Rightarrow f_1+12=20\Rightarrow f_1=8$
So the missing frequencies are $f_1=8and{f}_2=12$