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.

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