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Question
Find the mean and variance for the data.
| xi | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
| fi | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
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Solution
| xi | fi | fixi | `x_i - overline x` | `(x_i - overline x)^2` | `f_i (x_i - overline x)^2` |
| 6 | 2 | 12 | −13 | 169 | 338 |
| 10 | 4 | 40 | −9 | 81 | 324 |
| 14 | 7 | 98 | −5 | 25 | 175 |
| 18 | 12 | 216 | −1 | 1 | 12 |
| 24 | 8 | 192 | 5 | 25 | 200 |
| 28 | 4 | 112 | 9 | 81 | 324 |
| 30 | 3 | 90 | 11 | 121 | 363 |
| Sum | 40 | 760 | - | - | 1736 |
Mean `overline x = 760/40 = 19`
Variance `σ^2 = (sumf_i (x_i - overline x)^2)/N`
= `1736/40`
= 43.3
Hence, mean = 19, variance = 43.4
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