# 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

• $\sqrt{6}$

•   $\frac{52}{7}$

•  $\sqrt{\frac{52}{7}}$

#### 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