QQuestion
A life insurance agent found the following distribution of ages of 100 policy holders:
| Age (years) | 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) the number of policy holders whose age is above 52 years.
✓Answer
Use the upper class boundaries and cumulative frequencies to plot the less-than ogive.
Take 2 cm = 5 years on the x-axis and 2 cm = 10 policy holders on the y-axis.
Plot the points:
(20, 0), (25, 2), (30, 6), (35, 18), (40, 38), (45, 66), (50, 88), (55, 96) and (60, 100).
Join the plotted points with a smooth free-hand curve.
(a) Total number of policy holders, n = 100.
Median corresponds to the n/2th observation.
⇒ Median position = 100/2
⇒ Median position = 50th observation
From 50 on the cumulative-frequency axis, draw a horizontal line to meet the ogive. From that point, draw a vertical line to the age axis.
The graph gives the median age as approximately 42 years.
(b) From 52 years on the age axis, draw a vertical line to meet the ogive. From that point, draw a horizontal line to the cumulative-frequency axis.
The graph gives approximately 91 policy holders aged 52 years or below.
Number aged above 52 years = 100 − 91
⇒ Number aged above 52 years = 9
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