Question

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:

1. The median age.
2. Number of policy holders whose age is above 52 years.

Answer 1

1. Construct the Ogive

To draw a “less than“ ogive, we plot the cumulative frequency against the upper class boundaries of the age intervals.

Plotting Points: (20, 0), (25, 2), (30, 6), (35, 18), (40, 38), (45, 66), (50, 88), (55, 96), (60, 100).

Scale: Use 2 cm = 5 years on the x-axis and 2 cm = 10 policy holders on the y-axis as requested.

2. Find the median age

1. Locate median point: Since the total number of policy holders (N) is 100, the median is at the `N/2` = 50^th position.

2. Read from graph: From 50 on the y-axis, draw a horizontal line to the curve, then a vertical line down to the x-axis.

3. Result: The point on the x-axis is approximately 42.14 years.

3. Number of policy holders above 52 years

1. Locate age 52: Find 52 on the x-axis and draw a vertical line up to the curve.

2. Find cumulative frequency: Move horizontally to the y-axis. The cumulative frequency at age 52 is approximately 91.

3. Calculate remaining: To find those above age 52, subtract this value from the total: 100 – 91 = 9.

4. Result: Approximately 9 policy holders are older than 52 years.

The median age is 42.14 years and the number of policy holders above 52 years is 9.