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Question
Find the mean and variance for the first 10 multiples of 3.
Solution
First 10 multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
| xi | yi = `(x_i - 15)/3` | `y_i^2` |
| 3 | −4 | 16 |
| 6 | −3 | 9 |
| 9 | −2 | 4 |
| 12 | −1 | 1 |
| 15 | 0 | 0 |
| 18 | 1 | 1 |
| 21 | 2 | 4 |
| 24 | 3 | 9 |
| 27 | 4 | 16 |
| 30 | 5 | 25 |
| Sum | 5 | 85 |
Mean `overline x = "A" + (sumy_i)/n xx h`
= `15 + 5/10 xx 3`
= 15 + 1.5
= 16.5
Variance, `σ^2 = h^2/h^2 [n sum y_i^2 - (sum y_i)^2]`
= `9/100 [10 xx 85 - 25]`
= `9/100 [850 - 25]`
= `(9 xx 825)/100`
= `7425/100`
= 74.25
Hence, mean = 16.5, variance = 74.25
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