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For a set of values the mean is 6.3, the median is 6.5 and the mode is 7. Which way is the distribution skewed?
ASkewed to the right
BPerfectly symmetric
CSkewed to the top
DSkewed to the left
Answer & Solution
Correct answer: D. Skewed to the left
1. Compare the three figures in order of size.
2. The mean of 6.3 is the smallest, then the median of 6.5, then the mode of 7.
3. A mean below the median, with both below the mode, is the signature of a left skew.
4. The long tail runs off to the low side, which is what pulls the mean down.
5. A right skew would show the reverse order, with the mode smallest and the mean largest.
6. Perfectly symmetric data would put the mean and the median on the same value.
7. Skewed to the top is not a direction a distribution can take, since skew is read left or right.
_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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