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 ...
Question 1 Report
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.
Answer Details
Method. Assumed mean \(A = 1.45\), class width \(c = 0.2\), \(u = \dfrac{x - 1.45}{0.2}\) where \(x\) is the class midpoint.
| Length (m) | Midpoint \(x\) | \(u\) | \(f\) | \(fu\) |
|---|---|---|---|---|
| 1.0 - 1.1 | 1.05 | -2 | 2 | -4 |
| 1.2 - 1.3 | 1.25 | -1 | 3 | -3 |
| 1.4 - 1.5 | 1.45 | 0 | 8 | 0 |
| 1.6 - 1.7 | 1.65 | 1 | 5 | 5 |
| 1.8 - 1.9 | 1.85 | 2 | 2 | 4 |
| Total | 20 | 2 |
Mean.
\[ \bar{x} = A + \left(\frac{\sum fu}{\sum f}\right)c = 1.45 + \frac{2}{20}\times 0.2 = 1.45 + 0.02 = \mathbf{1.47 \text{ m}} \]Download The App On Google Playstore
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