Discussion
The sum of the deviations of a set of n values from their arithmetic mean is:
Answer: A
\[ \sum (x_{i} - \bar{x}) = \sum x_{i} - n\bar{x} = n\bar{x} - n\bar{x} = 0 \]
The deviations always cancel, which is exactly why the mean is the balance point of the data - and why absolute or squared deviations are used to measure spread.
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