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 years.

Question :

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

Solution :

We are given the cumulative frequency distribution.

So, we first construct a frequency table from the given cumulative frequency distribution and then we will make necessary computations to compute median.

Class Interval	Frequency	Cumulative Frequency
18 – 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

Here, n = 100 So, \(n\over 2\) = 50

We see that the cumulative frequency just greater than \(n\over 2\), i.e. 50 is 78 and the corresponding class is (35 – 40), So, it is the median class.

\(\therefore\) l = 35, cf = 45, f = 33 and h = 5.

Now, let us substitute these values in the formula

Median = l + (\({n\over 2} – cf\over f\)) \(\times\) h = 35 + \(5\over 33\) \(\times\) 5

= 35 + 0.76 = 35.76

Hence, the median age is 35.76 years.