Question

The mean of the following frequency table is $57.6$. But the frequencies $f_1$ and $f_2$ are missing. Find the value of missing frequencies $f_1$ and $f_2$.

Class Interval	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$	$100-120$	Total
Frequency	$7$	$f_1$	$12$	$f_2$	$8$	$5$	$50$

Answer 1

Class Interval	Frequency ( f)	Mid point x	fx
$0-20$	$7$	$10$	$70$
$20-40$	$f_1$	$30$	$30f_1$
$40-60$	$12$	$50$	$600$
$60-80$	$f_2$	$70$	$70f_2$
$80-100$	$8$	$90$	$720$
$100-120$	$5$	$110$	$550$
Total	$\sum f=32+f_2+f_2=50$		$\sum fx=30f{x}_1+70f_2+1940$

$\sum f=f_1+f_2+32=50$
$\Rightarrow f_1+f_2=18$ ..........(i)

Mean $\overline{x}=\frac{\sum fx}{\sum f}$

$57.6=\frac{30f_1+70f_2+1940}{50}$
$30f_1+70f_2+1940=2,880$
$30f_1+70f_2=940$
or $3f_1+7f_2=94$ .............(ii)

Solving (i) and (ii)
$f_1=8,f_2=10$

Thus, the value of $f_1$ is $8$ and the value of $f_2=10$.