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In a perfectly symmetrical distribution, how do the mean and the median compare?
AThe mean sits above the median
BThe mean sits below the median
CThe mean and the median are equal
DThe mean and the median are unrelated
Answer & Solution
Correct answer: C. The mean and the median are equal
1. Symmetry means the shape on the left of a central line mirrors the shape on the right.
2. Neither tail therefore pulls the mean away from the centre.
3. In a perfectly symmetrical distribution the mean and the median take the same value.
_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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