Question

A life insurance agent found the following data for the distribution of ages of $100$ policy holders. Calculate the median age, if policies are only given to persons having age $18$ years on wards but less than $60$ years.

Age in years	Number of policy holders
Below 20	$2$
Below 25	$6$
Below 30	$24$
Below 35	$45$
Below 40	$78$
Below 45	$89$
Below 50	$92$
Below 55	$98$
Below 60	$100$

Answer 1

Class interval	Frequency	Cumulative frequency
$15-20$	$2$	$2$
$20-25$	$4$	$6$
$25-30$	$18$	$24$
$30-35$	$21$	$45$
$35-40$	$33$	$78$
$40-45$	$11$	$89$
$45-50$	$3$	$92$
$50-55$	$6$	$98$
$55-60$	$2$	$100$

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

The cumulative frequency just greater then $50$ is $78$.

$\therefore$ Median class $=35-40$

Here, $l=35,h=5,f=33,cf=45$

$Median=l+\frac{\frac{N}{2}-cf}{f}\times h$

$\Rightarrow$ $Median=35+\frac{50-45}{33}\times 5$

$\Rightarrow$ $Median=35+\frac{25}{33}=35.76$