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...
Question 1 Report
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.
Answer Details
The assumed-mean (working-mean) method for grouped data uses \(\bar{x}=A+\dfrac{\sum fd}{\sum f}\), where \(d=x-A\), \(x\) is the class mid-value and \(A=24.5\) is the assumed mean.
Each class has width 4, so the mid-value is the average of the class limits, e.g. \(\tfrac{15+18}{2}=16.5\).
| Ages | Frequency \(f\) | Mid-value \(x\) | \(d=x-24.5\) | \(fd\) |
|---|---|---|---|---|
| 15 - 18 | 40 | 16.5 | -8 | -320 |
| 19 - 22 | 33 | 20.5 | -4 | -132 |
| 23 - 26 | 25 | 24.5 | 0 | 0 |
| 27 - 30 | 10 | 28.5 | 4 | 40 |
| 31 - 34 | 8 | 32.5 | 8 | 64 |
| 35 - 38 | 4 | 36.5 | 12 | 48 |
| Total | 120 | -300 |
\[\bar{x}=A+\frac{\sum fd}{\sum f}=24.5+\frac{-300}{120}=24.5-2.5=22.0\]
The mean age of the distribution is 22 years.
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