The table shows the distribution of the lengths of 20 iron rods measured in metres
FURTHER MATHEMATICS
WAEC 2014
The table shows the distribution of the lengths of 20 iron rods measured in metres :
| Length (m) | 1.0 - 1.1 | 1.2 - 1.3 | 1.4 - 1.5 | 1.6 - 1.7 | 1.8 - 1.9 |
| Frequency | 2 | 3 | 8 | 5 | 2 |
Using an assumed mean of 1.45, calculate the mean of the distribution.
Explanation
Assumed mean = 1.45
| Length (m) | Freq (f) | Mid-length (x) | \(d = x - A\) | \(fd\) |
| 1.0 - 1.1 | 2 | 1.05 | -0.4 | -0.8 |
| 1.2 - 1.3 | 3 | 1.25 | -0.2 | -0.6 |
| 1.4 - 1.5 | 8 | 1.45 | 0 | 0 |
| 1.6 - 1.7 | 5 | 1.65 | 0.2 | 1.0 |
| 1.8 - 1.9 | 2 | 1.85 | 0.4 | 0.8 |
| 20 | 0.4 |
Mean \(\bar{x} = A + \frac{\sum fd}{\sum f}\)
= \(1.45 + \frac{0.4}{20}\)
= \(1.45 + 0.02\)
= \(1.47\)
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