Question

The median of 230 observations is 46. Find $a$ and $b$.

Class	10-20	20-30	30-40	40-50	50-60	60-70
Frequency	12	30	$a$	65	$b$	25

Answer 1

Class	Frequency $\left(f\right)$	Cumulative Frequency $(c.f)$
$0-10$	$12$	$12$
$20-30$	$30$	$42$
$30-40$	$a$	$42+a$
$40-50$	$65$	$107+a$
$50-60$	$b$	$107+a+b$
$60-70$	$25$	$132+a+b$
Total $\left(N\right)$	$230$

Given: Median $=46$ and $\frac{N}{2}=\frac{230}{2}=115$

Hence, median class $\Rightarrow 40-50$

So, $L=40,h=10$, $f=65$ and $c.f=42+a$

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

$46=40+\frac{10}{65}(115-42-a)$

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

$\therefore a=73-39=34$

And, $132+34+b=230$

$b=64$