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The arithmetic mean is the first moment of a distribution. Which moments are the variance and the skewness?
AVariance is the third, skewness is the second
BVariance is the first, skewness is the third
CVariance is the second, skewness is the third
DVariance is the second, skewness is the fourth
Answer & Solution
Correct answer: C. Variance is the second, skewness is the third
1. The mean is the first moment and works with the raw values.
2. The variance squares the deviations from the mean, so it is the second moment.
3. Skewness cubes those deviations, so it is the third moment.
4. The rising power of the deviation is what numbers each moment.
5. Calling variance the third moment would require it to cube the deviations, which it does not.
6. Calling skewness the fourth moment would require a further power beyond the cube.
_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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