Question

The mean of the following frequency table 50. But the frequencies $f_1$ and $f_2$ in class 20-40 and 60-80 are missing. Find the missing frequencies.

Class:	0-20	20-40	40-60	60-80	80-100	Total
Frequency:	17	$f_1$	32	$f_2$	19	120

Answer 1

Class $f_1$	Frequency $x_i$	Mid-values	$u_i=\frac{x_i-A}{h}$	$f_i{u}_i$
$0-20$	$17$	$10$	$-2$	$-34$
$20-40$	$f_1$	$30$	$-1$	$-f_1$
$40-60$	$32$	$50$	$0$	$0$
$60-80$	$f_2$	$70$	$1$	$-f_2$
$80-100$	$19$	$90$	$2$	$38$
	N= $\sum f_i=63+f_1+f_2$			$\sum f_i{u}_i=4-f_1+f_2$

We have,
$N=\sum f_i=120$ [Given]
$\Rightarrow 68+f_1+f_2=120$
$\Rightarrow f_1+f_2=52$
Now,

Mean = 50
$\Rightarrow A+h[\frac{1}{N}\sum f_i{u}_i]=50$

$\Rightarrow 50+20\times \left[\frac{4-f_1+f_2}{120}\right]=50$

$\Rightarrow \frac{4-f_1+f_2}{6}=0$

$\Rightarrow 4-f_1+f_2=0$

$\Rightarrow f_1-f_2=4$
Solving equations (i) and (ii), we get $f_1$ = 28 and $f_2=24$.