The table shows the distribution of the ages of a group of people in a village.
| Ages (in years) | 15 – 18 | 19 – 22 | 23 – 26 | 27 – 30 | 31 – 34 | 35 – 38 |
| Frequency | 40 | 33 | 25 | 10 | 8 | 4 |
Using an assumed mean of 24.5, calculate the mean of the distribution.
Explanation
|
Age interval (years) |
Class midpoint (x) |
Freq (f) | d = x – A | fd |
| 15 – 18 | 16.5 | 40 | -8.0 | -320.0 |
| 19 – 22 | 20.5 | 33 | -4.0 | -132.0 |
| 23 – 26 | 24.5 | 25 | 0 | 0 |
| 27 – 30 | 28.5 | 10 | 4.0 | 40.0 |
| 31 – 34 | 32.5 | 8 | 8.0 | 64.0 |
| 35 – 38 | 36.5 | 4 | 12.0 | 48.0 |
| Total | 120 | -300.0 |
(Mean, (bar {x}) = A + frac{sum fd}{sum f})
= (24.5 + frac{-300}{120})
= (24.5 – 2.5)
= 22.0