Question

If \(\overline{x}\) is the mean of \(n\) observations \(x_1, x_2, x_3, \ldots, x_n\), then \(\sum_{i=1}^{n}(x_i - \overline{x})\) is equal to

• A. 1
• B. 0
• C. None of these
• D. \(\infty\)

Hint:

When finding the sum of deviations from the mean, the result will always be zero.

Answer 1

The Correct Option is B

The sum of deviations from the mean is always 0, i.e.: \[ \sum_{i=1}^{n}(x_i - \overline{x}) = 0 \] This is because the mean \(\overline{x}\) is defined such that the sum of deviations from it is 0. Thus, the correct answer is 0.