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Which statement correctly contrasts the variance with the skewness?
ABoth can take negative values in practice
BNeither can ever take a negative value
CVariance can be negative but skewness cannot
DSkewness can be negative but variance cannot
Answer & Solution
Correct answer: D. Skewness can be negative but variance cannot
1. The variance averages squared deviations, and a square is never negative.
2. Skewness averages cubed deviations, and a cube keeps the sign of the deviation.
3. So skewness can come out negative while the variance cannot.
4. That sign is exactly what tells you whether the data are skewed left or right.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.6 Skewness and the Mean, Median, and Mode_
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