Problem-Solving and Data AnalysisHardSame mean, different spread
Problem-Solving and Data Analysis practice question
Data set P consists of the values 10, 20, 30, 40. Data set Q consists of the values 22, 24, 26, 28. Which statement is true?
- A. The two data sets have the same mean, but P has the larger standard deviation.Correct
- B. The two data sets have the same mean and the same standard deviation.
- C. P has the larger mean and the larger standard deviation.
- D. Q has the larger mean, but P has the larger standard deviation.
Answer: A. The two data sets have the same mean, but P has the larger standard deviation.
Both sets have mean 25 (100/4). P's values are spread from 10 to 40, Q's only from 22 to 28, so P's standard deviation is larger.
Why the other answers are wrong
- B. The two data sets have the same mean and the same standard deviation.
- The means match, but the spreads clearly differ.
- C. P has the larger mean and the larger standard deviation.
- The means are equal: 100/4 = 25 for both.
- D. Q has the larger mean, but P has the larger standard deviation.
- Q's mean is also 25, not larger.
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