Question

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

Age (in years)	No. 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 $60$	$100$

• A. $62.12$ years
• B. $53.53$ years
• C. $35.76$ years
• D. None of these

Answer 1

Answer: (C)

$35.76$ years

Age (in years)	Number of policy holders $f_1$	Cumulative frequency
Below $20$	$2=2$	$2$
$20-25$	$(6-2)=4$	$6$
$25-30$	$(24-6)=18$	$24$
$30-35$	$(45-24)=21$	$45$
$35-40$	$(78-45)=33$	$78$
$40-45$	$(89-78)=11$	$89$
$45-50$	$(92-89)=3$	$92$
$50-55$	$(98-92)=6$	$98$
$55-60$	$(100-98)=2$	$100$
Total	$n=100$

Here, $l=35,n=100,f=33,cf=45,h=5$ Median$=l+\left\{\frac{\frac{n}{2}-cf}{f}\right\}\times h$

$=35+\left\{\frac{50-45}{33}\right\}\times 5$

$=35+\frac{25}{33}$

$=35+0.76$

$=35.76$ years