Problem-Solving and Data AnalysisHardSet whose mean exceeds its median
Problem-Solving and Data Analysis practice question
For which of the following data sets is the mean GREATER than the median?
- A. 1, 2, 3, 10Correct
- B. 1, 2, 3, 4
- C. 1, 8, 9, 10
- D. 5, 5, 5, 5
Answer: A. 1, 2, 3, 10
1, 2, 3, 10 has median (2 + 3)/2 = 2.5 and mean 16/4 = 4. The large value 10 pulls the mean above the median.
Why the other answers are wrong
- B. 1, 2, 3, 4
- 1, 2, 3, 4 is evenly spaced: mean and median are both 2.5.
- C. 1, 8, 9, 10
- 1, 8, 9, 10 has median 8.5 and mean 7 — the small value pulls the mean BELOW the median.
- D. 5, 5, 5, 5
- All values equal: mean and median are both 5.
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