# Aptitude Question ID : 94176

The average of n numbers $x_{1}, x_{2}, ...., x_{n}$ is $\overline{x}$. Then the value of $\sum_{i=1}^{n}(x_{i} - \overline{x})$ is equal to :
[A]$0$
[B]$\overline{x}$
[C]$n\overline{x}$
[D]$n$

$\mathbf{0}$
$\because \frac{x_{1}+x_{2}+....+x_{n}}{n} = \overline{x}$
$\therefore \sum_{i=1}^{n}(x_{i} - \overline{x})$
$= (x_{1} - \overline{x})+(x_{2} - \overline{x})+......+(x_{n} - \overline{x})$
$= (x_{1}+x_{2}+......+x_{n}) - n\overline{x}$
$= n. \left ( \frac{x_{1}+x_{2}+....+x_{n}}{n} \right )- n\overline{x}$
$= n\overline{x}- n\overline{x} = 0$
Hence option [B] is the right answer.