The table shows the distribution of the ages of a group of people in a...
FURTHER MATHEMATICSWAEC 2006
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
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