Question

The age of the population in Wakanda is shown in the following table in the form of a

grouped frequency distribution.

Age (years) Number (‘000)

0 Under 5 1 375.3

5 under 15 2 750.5

15 under 30 4 514.7

30 under 50 6 137.7

50 under 65 3 821.7

65 under 80 2 045.7

80 under 100 783.2

100 under 110 3.1

Total 21 431.8

Use the data in the table above to estimate for of population in Wakanda the:

BACHELOR OF COMMERCE YEAR 1 – ACADEMIC AND ASSESSMENT CALENDAR - DISTANCE

REGENT BUSINESS SCHOOL (RBS) – JANUARY 2021 15

3.1 median age.

Answer 1

Median number:

$m=n/2=21431.9/2=10715.95$

Median class$=|30-50|=20$

Median age:

$M=l_1+\frac{n/2-cf}{f}\cdot i$

where $l_1$ is lower number of median class,

$cf$ is cumulative frequency of class preceding to median class,

$f$ is frequency/number of median class,

$i$ is class length.

$M=30+\frac{10715.95-8640.5}{6137.7}\cdot20=36.76$

So, median age is 36.76 years.