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

Cumulative frequency distribution table is as follows :

Here, n = 100, $\dfrac{n}{2} = 50$.

Cumulative frequency just greater than 50 is 78, belonging to class-interval 35 − 40.

Therefore, median class = 35 - 40

⇒ Class size (h) = 5

⇒ Lower limit of median class (l) = 35

⇒ Frequency of median class (f) = 33

⇒ Cumulative frequency of class preceding median class (cf) = 45

By formula,

Median = $l + \Big(\dfrac{\dfrac{n}{2} - cf}{f}\Big) \times h$

Substituting values we get :

$\Rightarrow \text{Median } = 35 + \dfrac{50 - 45}{33} \times 5 \\[1em] = 35 + \dfrac{25}{33} \\[1em] = 35 + 0.76 \\[1em] = 35.76$

Hence, median age = 35.76 years.