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Question
The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is
Options
6
\[\sqrt{6}\]
\[\frac{52}{7}\]
\[\sqrt{\frac{52}{7}}\]
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Solution
The given observations are 6, 5, 9, 13, 12, 8, 10.
Now,
\[\sum_{} x_i = 6 + 5 + 9 + 13 + 12 + 8 + 10 = 63\]
\[\sum_{} x_i^2 = 36 + 25 + 81 + 169 + 144 + 64 + 100 = 619\]
∴ Standard deviation of the observations,
\[ = \sqrt{\frac{1}{7} \times 619 - \left( \frac{1}{7} \times 63 \right)^2}\]
\[ = \sqrt{\frac{619}{7} - 81}\]
\[ = \sqrt{\frac{619 - 567}{7}}\]
\[ = \sqrt{\frac{52}{7}}\]
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