Question

If the mean of n observations $x_1,x_2$, ....... $x_n$ is $\overline{x}$,then the sum of deviations of observations from mean is

• A. $0$
• B. n$\overline{x}$
• C. $\frac{\overline{x}}{n}$
• D. none of these

Answer 1

The correct option is A $0$

$\because \frac{x_1+x_2.....+x_n}{n}=\overline{x}$ .......... (i)

$\therefore$ Req. sum $=(x_1-\overline{x})+(x_2-\overline{x})+......+(x_n-\overline{x})$

$=(x_1+x_2+......x_n)-n\overline{x}$

$=n\overline{x}-n\overline{x}=0$ (from eq. (i))