(C) Given: $n = 10$,$\sum x_i = 12$,and $\sum x_i^2 = 18$. The formula for standard deviation $(\sigma)$ is: $\sigma = \sqrt{\frac{\sum x_i^2}{n} - \l

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(C) Given: $n = 10$,$\sum x_i = 12$,and $\sum x_i^2 = 18$. The formula for standard deviation $(\sigma)$ is: $\sigma = \sqrt{\frac{\sum x_i^2}{n} - \left(\frac{\sum x_i}{n}\right)^2}$ Substituting the given values: $\sigma = \sqrt{\frac{18}{10} - \left(\frac{12}{10}\right)^2}$ $\sigma = \sqrt{1.8 - (1.2)^2}$ $\sigma = \sqrt{1.8 - 1.44}$ $\sigma = \sqrt{0.36}$ $\sigma = 0.6 = \frac{6}{10} = \frac{3}{5}$

Class 11 Mathematics Statistics Variance and Standard Deviation

Medium

If the sum of $10$ observations and the sum of their squares are $12$ and $18$ respectively,then the standard deviation of the observations is:

A
$\frac{1}{5}$
B
$\frac{2}{5}$
C
$\frac{3}{5}$
D
$\frac{4}{5}$

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Variance and Standard Deviation

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If the sum of $10$ observations and the sum of their squares are $12$ and $18$ respectively,then the standard deviation of the observations is:

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