Problem-Solving and Data AnalysisVery hardEffect on mean and median of raising the largest value
Problem-Solving and Data Analysis practice question
A data set has five values with a mean of 20 and a median of 18. The largest value is increased by 10 and the other values are unchanged. Which of the following describes the new mean and median?
- A. The mean rises to 22, and the median is unchanged at 18.Correct
- B. The mean and the median both rise by 10.
- C. The mean is unchanged, and the median rises to 28.
- D. The mean rises to 30, and the median rises to 20.
Answer: A. The mean rises to 22, and the median is unchanged at 18.
The total rises by 10, so the mean rises by 10/5 = 2; the middle value is untouched.
Why the other answers are wrong
- B. The mean and the median both rise by 10.
- The median does not depend on how large the largest value is.
- C. The mean is unchanged, and the median rises to 28.
- The mean changes; the median does not.
- D. The mean rises to 30, and the median rises to 20.
- The mean rises by 2, not 10.
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