A life insurance agent found the following data for distribution of ages of 100 policy holders.

Solution:

We prepare the cumulative frequency, table as given below.

Now, we have

$N=100$

So, $\frac{N}{2}=50$

Now, the cumulative frequency just greater than 50 is 78 and the corresponding class is $35-40$.

Therefore, $35-40$ is the median class.

Here, $l=35, f=33, F=45$ and $h=5$

We know that

Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$

$=35+\left\{\frac{50-45}{33}\right\} \times 5$

$=35+\frac{5 \times 5}{33}$

$=35+\frac{25}{33}$

$=35+0.76$

 

$=35.76$

Hence, the median age is 35.76 years.