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Question
Find the mean, variance and standard deviation for the data:
2, 4, 5, 6, 8, 17.
Solution
2,4,5,6,8,17
\[\text{ Mean } = \bar{ X } = \frac{2 + 4 + 5 + 6 + 8 + 17}{6} = \frac{42}{6} = 7\]
|
\[x_i\]
|
\[\left( x_i - X \right) = \left( x_i - 7 \right)\]
|
\[\left( x_i - 7 \right)^2\]
|
|---|---|---|
| 2 | -5 | 25 |
| 4 | -3 | 9 |
| 5 | -2 | 4 |
| 6 | -1 | 1 |
| 8 | 1 | 1 |
| 17 | 10 | 100 |
|
\[\sum^6_{i = 1} \left( x_i - X \right)^2 = 140\]
|
n =6
\[\text{ Variance } (X) = \frac{\sum^6_{i = 1} \left( x_i - X \right)^2}{n}\]
\[ = \frac{140}{6}\]
\[ = 23 . 33\]
\[\text{ Standard deviation } = \sqrt{\text{ Variance }(X}) \]
\[ = \sqrt{23 . 33}\]
\[ = 4 . 83\]
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