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

Age in years	Policy holders (frequency)	Cumulative frequency
20-25	2	2
25-30	4	6
30-35	12	18
35-40	20	38
40-45	28	66
45-50	22	88
50-55	8	96
55-60	4	100

On a graph sheet draw an ogive using the given data. Take 2 cm = 5 years along one axis and 2 cm = 10 policy holders along the other axis. Use your graph to find:

(a) The median age.

(b) Number of policy holders whose age is above 52 years.

Steps of construction :

1. Take 2 cm = 5 years on x-axis.

2. Take 1 cm = 10 policy holders on y-axis.

3. Plot the points (20, 0), (25, 2), (30, 6), (35, 18), (40, 38), (45, 66), (50, 88), (55, 96) and (60, 100).

4. Join the points by a free-hand curve.

Here, n = 100

Median = $\dfrac{n}{2} = \dfrac{100}{2}$ = 50th term

(a) Through J = 50 draw a horizontal line to meet the ogive at K. Through K, draw a vertical line to meet the x-axis at L. The abscissa of the point L represents 42.

Hence, the median age = 42 years.

(b) Through M = 52 draw a vertical line to meet the ogive at N. Through N, draw a horizontal line to meet the y-axis at O. The ordinate of the point O represents 91.

Hence, 91 people have their age less than or equal to 52.

∴ No. of people whose age is greater than 52 = 100 - 91 = 9.

Hence, number of policy holders whose age is above 52 years equal to 9.