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In a perfectly symmetrical distribution, what is true of the mean and the median?
AThey are far apart
BThey are both zero
CThey are both modes
DThey are the same
Answer & Solution
Correct answer: D. They are the same
1. A symmetrical graph looks the same on both sides of a central line.
2. Neither tail is longer, so nothing pulls the mean away from the middle.
3. The mean and the median therefore land on the same value.
4. They need not be zero, since the value depends entirely on the data.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics" and Ch 3 "Probability Topics", section 2.6 Skewness and the Mean, Median, and Mode_
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