Question

The mean of observations $x_1$, $x_2$, $x_3$, ..., $x_n$ is $\overline{x}$. then the value of
$(x_1-\overline{x})+(x_2-\overline{x})+...+(x_n-\overline{x})$ equals

• A. $(n-1)\overline{x}$
• B. $n\overline{x}$
• C. $(n+1)\overline{x}$
• D. None of these

Answer 1

The correct option is D None of these

$(x_1-\overline{x})+(x_2-\overline{x})+...+(x_n-\overline{x})$
$=(x_1+x_2+x_3+...+x_n)-\underset{ntimes}{\underset{}{(\overline{x}+\overline{x}+...+\overline{x})}}$
$=n\overline{x}-n\overline{x}=0$