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Question
Find the mean, variance and standard deviation for the data:
6, 7, 10, 12, 13, 4, 8, 12.
Solution
6,7,10,12,13,4,8,12
\[\text{ Mean } = \frac{6 + 7 + 10 + 12 + 13 + 4 + 8 + 12}{8}\]
\[ = \frac{72}{8}\]
\[ = 9\]
|
\[x_i\]
|
\[\left( x_i - X \right) = \left( x_i - 9 \right)\]
|
|
|---|---|---|
| 6 | -3 | 9 |
| 7 | -2 | 4 |
| 10 | 1 | 1 |
| 12 | 3 | 9 |
| 13 | 4 | 16 |
| 4 |
|
25 |
| 8 |
|
1 |
| 12 | 3 | 9 |
|
|
n = 8
\[\therefore \text{ Variance } \left( X \right) = \frac{\sum^8_{i = 1} \left( x_i - X \right)^2}{n}\]
\[ = \frac{74}{8} \]
\[ = 9 . 25\]
\[\text{ Standard deviation }= \sqrt{\text{Variance} \left( X \right)} \]
\[ = \sqrt{9 . 25} \]
\[ = 3 . 04\]
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