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# 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 holder 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

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 15-20 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 $$n \ = \ \sum f_i \ = \ 100 \ => \ \frac{n}{2} \ = \ 50$$

We see that the cumulative frequency just greater than $$\frac{n}{2}$$, i.e., 50 is 78 and the corresponding class is 35 - 40.

So, 35 - 40 is the median class.

$$\therefore \frac{n}{2} \ = \ 50 , l = 35, c.f = 45 , f = 33, h = 5$$

Now, let us substitute these values in the formula

Median $$= \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h$$

$$= \ 35 \ + \ \frac{50 \ - \ 45}{33} \ × \ 5$$

$$= \ 35 \ + \ \frac{5}{33} \ × \ 5$$

$$= \ 35 \ + \ 0.76 \ = \ 35.76$$

$$\therefore$$ The median age = 35.76 years