Question

If $\overline{x}$ is the mean of the terms $x_1,x_2,x_3\dots x_n$ and $\sum _{i=1}^n{x}_i=x_1+x_2+x_3+\dots x_n$ then the value of $\sum _{i=1}^n{x}_i-n\overline{x}$ is

• A. $0$
• B. $1$
• C. $n$
• D. $x$

Answer 1

Answer: (A)

$0$

$\overline{x}=\frac{x_1+x_2+x_3+\dots x_n}{n}$....(1)
$\sum _{i=1}^n(x_i-n\overline{x})=(x_1+x_2+x_3+\dots x_n)-n\overline{x}$
$=n\overline{x}-n\overline{x}=0$ (from 1)