Question

The median of the distribution given is $46$. Find the values of $x$ and $y$, if the total frequency is $230$.

Class Interval	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Number of students	$12$	$30$	x	$65$	y	$25$	$18$

Answer 1

Class $fi$ $C.F$

$10-20$ $12$ $12$

$20-30$ $30$ $42$

$30-40$ $x$ $42+x$

$40-5065107+x$ Median class

$50-60$ $7$ $107+x+y=107+80=187$

$60-70$ $25$ $132+x+y=132+80=212$

$70-80$ $18$ $150+x+y=230$

A/Q, $N=230$

$\Rightarrow$ $x+y=80$

$\frac{N}{2}=115$

Median $=40+\frac{115-42-x}{65}\times 10$

$\Rightarrow \frac{73-x}{65}\times 10=6$

$\Rightarrow 73-x=\frac{65\times 6}{10}$

$\Rightarrow 73-x=39$

$\Rightarrow x=34$ $\therefore$ $y=46$