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Question
Find the mean, variance and standard deviation for the data 15, 22, 27, 11, 9, 21, 14, 9.
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Solution
15,22,27,11,9,21,14,9
\[\text{ Mean } = \frac{15 + 22 + 27 + 11 + 9 + 21 + 14 + 9}{8} = \frac{128}{8} = 16\]
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\[x_i\]
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\[\left( x_i - X \right) = \left( x_i - 16 \right)\]
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\[\left( x_i - \bar{X} \right)^2\]
|
|---|---|---|
| 15 | −1 | 1 |
| 22 | 6 | 36 |
| 27 | 11 | 121 |
| 11 | 5 | 25 |
| 9 | −7 | 49 |
| 21 | 5 | 25 |
| 14 | −2 | 4 |
| 9 | −7 | 49 |
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\[\sum^8_{i = 1} \left( x_i - \bar{X} \right)^2 = 310\]
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\[\therefore n = 8\]
\[\text{ Variance } \left( X \right) = \frac{\sum^8_{i = 1} \left( x_i - x \right)^2}{n} \]
\[ = \frac{310}{8}\]
\[ = 38 . 75\]
\[\text{ Standard deviation } = \sqrt{ \text{ Variance } \left( X \right)} \]
\[ = \sqrt{38 . 75} \]
\[ = 6 . 22\]
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