Question

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

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

Here, the width of the square is not uniform. There is no need to adjust the frequencies according to the class interval. The given frequency table is less than the type shown with higher class boundaries. The policy was offered only to individuals above 18 years of age but below 60 years of age. Therefore, the class intervals with their respective cumulative frequencies can be defined as follows:

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

From the table, it can be seen that n = 100.

The cumulative frequency (cf) is more than `n/2(100/2 = 50) 78`,

Which corresponds to the interval 35 – 40. Hence, median class = 35 – 40 Lower limit of median class (l) = 35 class.

Size (h) = 5 Frequency of median class (f) = 33 Cumulative frequency of classes preceding the median class (cf) = 45.

Median =` l + ((n/2-cf)/f)xxh`

= `35 + ((50-45)/33)xx5`

= `35 + 25/33`

= 35.76

Therefore, the average age is 35.76 years.