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For the data 6, 7, 7, 7, 7, 8, 8, 8, 9, 10 the median is 7.5 and the mode is seven. What is the mean, and what does it show?
AThe mean is 7.7, so it is the largest
BThe mean is 7.2, so it is the smallest
CThe mean is 7.5, so it ties the median
DThe mean is 8.0, so it equals the mode
Answer & Solution
Correct answer: A. The mean is 7.7, so it is the largest
1. The ten values add to 6 plus 28 plus 24 plus 9 plus 10, which is 77.
2. Dividing 77 by 10 gives a mean of 7.7.
3. That mean exceeds the median of 7.5, which in turn exceeds the mode of 7, the pattern of a right skew.
4. A mean of 7.5 would tie the median, which only happens when the distribution is symmetrical.
_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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