Question

If the mean and S.D. of n observations $x_1,x_2,....x_{n}are\overline{x}and\sigma$ resp, then the sum of squares of observations is

• A. $n({\sigma }^2+{\overline{x}}^2)$
• B. $n({\sigma }^2-{\overline{x}}^2)$
• C. $n({\overline{x}}^2-{\sigma }^2)$
• D. None of these

Answer 1

The correct option is A $n({\sigma }^2+{\overline{x}}^2)$

We know S.D of distribution is given by, $\sigma =\sqrt{\frac{\Sigma x_1^2}{n}-{\left(\frac{\Sigma x_1}{n}\right)}^2}=\sqrt{\frac{\Sigma x_1^2}{n}-\overline{x^2}}$
$\therefore \Sigma x_1^2=n({\sigma }^2+\overline{x^2})$