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The Standard Deviation of the Observations 6, 5, 9, 13, 12, 8, 10 is - Mathematics

MCQ

The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is

Options

  • \[\sqrt{6}\]

  •   \[\frac{52}{7}\]

  •  \[\sqrt{\frac{52}{7}}\]

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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,

\[\sigma\] \[= \sqrt{\frac{1}{N} \sum_{} x {}_i^2 - \left( \frac{1}{N} \sum_{} x_i \right)^2}\]

\[ = \sqrt{\frac{1}{7} \times 619 - \left( \frac{1}{7} \times 63 \right)^2}\]

\[ = \sqrt{\frac{619}{7} - 81}\]

\[ = \sqrt{\frac{619 - 567}{7}}\]

\[ = \sqrt{\frac{52}{7}}\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Q 25 | Page 52
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