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 persons 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. $47.12$ years
• B. $15.65$ years
• C. $25.17$ years
• D. $35.76$ years

Answer 1

The correct option is D $35.76$ years

Class Interval	No. of policy Holders Freq (Fi)	XI
18 to 20	2	2
20 to 25	4	6
25 to 30	18	24
30 to 35	21	45
35 to 40	33	78
40 to 45	11	89
45 to 50	3	92
50 to 55	6	98
55 to 60	2	100
	$N=100$

For continuous data, median

$=L+\left(\frac{\frac{N}{2}-C}{f}\right)\times H$

Where $N$ = Total cumulative frequency

$L$ = lower limit of the median class Interval;

Median Class = the class interval having cumulative

$freq\ge \frac{N}{2}$

$C=$ cumulative frequency of the class interval just before the median class interval

$f=$ frequency of the median class interval;

$H=$ width of the median class interval
Here $N=100\frac{N}{2}=50$

this cumulative freq lies within interval $(35-40);L=35;C=45;f=33;H=5$

Hence median $=35+(\frac{\frac{100}{2}-45}{33}\times 5)=35+(\frac{50-45}{33}\times 5)=35+\left(\frac{25}{33}\right)=35+0.7575=35+.76=35.76$