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If you add up all the deviations of the values from their mean, what do you get?
AYou get the variance of the data set
BYou get the range of the data set
CYou get the total of the data values
DYou get zero, whatever the data set
Answer & Solution
Correct answer: D. You get zero, whatever the data set
1. A deviation is a value minus the mean, and it is positive above the mean and negative below it.
2. The positive and negative deviations cancel exactly, because the mean is the balance point.
3. Their sum is therefore always zero, whatever the data set.
4. That is precisely why the deviations are squared before they are averaged into the variance.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.7 Measures of the Spread of the Data_
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