Problem-Solving and Data AnalysisHardComparing spread with equal means
Problem-Solving and Data Analysis practice question
Two data sets have the same mean. Set P: 10, 11, 12, 13, 14. Set Q: 2, 8, 12, 16, 22. Which of the following is true?
- A. Set Q has the larger standard deviation.Correct
- B. Set P has the larger standard deviation.
- C. The two sets have the same standard deviation.
- D. The two sets have different means.
Answer: A. Set Q has the larger standard deviation.
Both means are 12. Q's values are spread from 2 to 22, far from the mean; P's stay within 2 of it. So Q's standard deviation is larger.
Why the other answers are wrong
- B. Set P has the larger standard deviation.
- P's values cluster tightly around 12.
- C. The two sets have the same standard deviation.
- Different spreads give different standard deviations.
- D. The two sets have different means.
- Both sets sum to 60 across 5 values: mean 12.
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