Mathematics - Statistics Question with Solution | TestHub

SD, $\sigma =\sqrt{\frac{\sum x_i^2}{n}-{\left(\frac{\sum x_i}{n}\right)}^2}$

SD is independent of change of origin, so, for given data
$\sigma =\sqrt{\frac{\Sigma {\left(x_i-a\right)}^2}{n}-{\left(\frac{\Sigma \left(x_i-a\right)}{n}\right)}^2}$
$=\sqrt{\frac{na}{n}-{\left(\frac{n}{n}\right)}^2}=\sqrt{a-1}$