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For the data 11, 11, 12, 12, 12, 12, 13, 15, 17, 22, 22, 22 the mode is 12 and the median is 12.5. Which measure of centre is greatest?
AThe mode, at a value of 12.0
BThe median, at a value of 12.5
CThe mean, at a value of 15.1
DAll three take the same value
Answer & Solution
Correct answer: C. The mean, at a value of 15.1
1. The twelve values add to 22 plus 48 plus 13 plus 15 plus 17 plus 66, which is 181.
2. Dividing 181 by 12 gives a mean of about 15.1.
3. That mean exceeds the median of 12.5 and the mode of 12.
4. The three 22s form a long right tail that pulls the mean up but barely moves the median.
5. The mode of 12 is the smallest of the three, so it cannot be the greatest.
6. The three values differ, so they cannot all be the same.
_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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