Question

Find the missing frequencies:

C.I	0-10	10-20	20-30	30-40	40-50	50-60
f	10	$f_1$	25	30	$f_2$	10

$\sum f=100,median=32$

Answer 1

$CI$	$f$	$c.f$
$0-10$	$10$	$10$
$10-20$	$f_1$	$10+f_1$
$20-30$	$25$	$35+f_1$
$30-40$	$30$	$65+f_1$
$40-50$	$f_2$	$65+f_{+}{f}_2$
$50-60$	$10$	$75+f_1+f_2$
	$\sum f=75+x+y$

$\Rightarrow$ Here, $N=100$ and $\frac{100}{2}=50$

Here, Median class $=30-40$

$\Rightarrow$ $c.f=35+f_1,f=30,L=30$ and $h=10$

We know, $75+f_1+f_2=100$

$\therefore$ $f_1+f_2=25$ ------ ( 1 )

$\Rightarrow$ $Median=L+\left(\frac{\frac{N}{2}-c.f}{f}\right)\times h$

$\Rightarrow$ $32=30+\left(\frac{50-35-f_1}{30}\right)\times 10$

$\Rightarrow$ $2=\frac{50-35-f_1}{3}$

$\Rightarrow$ $6=15-f_1$

$\Rightarrow$ $f_1=9$

Put $f_1$ value in eq ( 1 )

$9+f_2=25$

$\therefore$ $f_2=16$

$\therefore$ $f_1=9$ and $f_2=16$