alleryStart learning →A data set has a mean of 5 and a standard deviation of 2. Which value sits 1.5 standard deviations above the mean?
AExactly 7
BExactly 8
CExactly 9
DExactly 6.5
Answer & Solution
Correct answer: B. Exactly 8
1. A value equals the mean plus a number of standard deviations times the standard deviation.
2. Here the number of standard deviations is 1.5 and each one is worth 2.
3. Multiply 1.5 by 2 to get 3.
4. Add that to the mean of 5.
5. 5 plus 3 is 8.
6. Answering 7 uses one standard deviation instead of one and a half.
7. Answering 9 uses two standard deviations.
8. Answering 6.5 adds 1.5 directly and forgets to scale it by the standard deviation.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics" and Ch 3 "Probability Topics", section 2.7 Measures of the Spread of the Data_
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