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Q. The standard deviation of the data $6, 7, 8, 9, 10$ is

KCETKCET 2020Statistics

Solution:

Mean, $\bar{x} = \frac{6+7+8+9+10}{5} = \frac{40}{5} = 8$
Standard deviation, $\sigma = \sqrt{\frac{1}{5}(4+1+0+1+4)}$
Because, $\sigma = \sqrt{\frac{1}{n} \sum(x_i - \bar{x})^2}$
$\Rightarrow \sigma = \sqrt{\frac{10}{5}} = \sqrt{2}$