(Q5) A life insurance agent found the following data about distribution of ages of 100 policy holders. Calculate the median age. [Policies are given only to persons having age 18 years onwards but less than 60 years].

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

Answer :

Age (in years)	Number of Policy Holders	Cumulative Frequency
Below 20	2	2
Below 25(20-25)	4	6
Below 30(25-30)	18	24
Below 35(30-35)	21	45 cf
Below 40(35-40) (l)	33 f	78
Below 45(40-45)	11	89
Below 50(45-50)	3	92
Below 55(50-55)	6	98
Below 60(55-60)	2	100

The given distribution being of the less than type 25, 30, 35, give the upper limits of corresponding class intervals. So the classes should be 20-25, 25-30, 30-35,....55-60.

Observe that from the given distribution 2 persons with age less than 20.

i.e., frequency of the class below 20 is 2.

Now there are 6 persons with age less than 25 and 2 persons with age less than 20.

∴The number of persons with age in the interval 20-25 is 6-2 = 4.

Similarly, the frequencies can be calculated as shown in table.

Number of observations = 100

n =

∴ 35-40 is the median class and lower boundary l = 35

cf = 45; h = 5; f = 33

∴ Median = .7575