Question

If $\overline{x}$ is the mean of the terms $x_1,x_2,x_3,...x_n$ and
$\sum _{i=1}^n{x}_1=x_1,x_2,x_3+......x_n$, then the value of $\sum _{i=1}^n{x}_i-n\overline{x}$

• A. $0$
• B. $1$
• C. $n$
• D. $x$

Answer 1

Answer: (A)

$0$

$\overline{x}=\frac{x_1+x_2+x_3+...+x_n}{n}$ (Given)
and $\sum _{i=1}^n{x}_i=x_1+x_2+......+x_n$ (Given)
Then $\sum _{i=1}^n{x}_i-\overline{nx}$ $=(x_1+x_2+......+x_n)$
$-n\frac{(x_1+x_2+......+x_n)}{n}$
$=0$