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Q. The standard deviation of $ 1,3, 5,7 $ is

J & K CETJ & K CET 2016Statistics

Solution:

Mean $ = \frac{1+3+5+7}{4} = 4$
$\therefore $ Variance
$= \sum\limits_{i=1}^4 \frac{(x_i - \bar{x})^2}{n}$
$ = \frac {(-3)^2 + (-1)^2 +(1)^2 +3^2}{4} = 5$
So, standard deviation $ = \sqrt{5}$