Question

The median of the following distribution is

Class interval	35-45	45-55	55-65	65-70
Frequency	8	12	20	10

• A. 56.5
• B. 57.5
• C. 58.7
• D. 59

Answer 1

The correct option is B 57.5

Class interval	Frequency	Cumulative frequency
$35-45$	$8$	$8$
$45-55$	$12$	$8+12=20$
$55-65$	$20$	$20+20=40$
$65-70$	$10$	$40+10=50$
	Total$\left(N\right)=50$

$N=50$
$\therefore \frac{N}{2}=25$
$⟹$ Median lies in the class $55-65$

Now, median $=l_1+\left[\frac{\frac{N}{2}-cf}{f}\right]\times h$
where, $l_1=$ lower limit of the median class

$f=$ frequency of the median class

$h=$ width (size) of the median class

$cf=$ cumulative frequency of the class preceding the median class

$\therefore$ Median $=55+\left[\frac{\frac{50}{2}-20}{20}\right]\times 10=57.5$

Hence, option B is correct.