Problem-Solving and Data AnalysisVery hardEffect of an outlier on mean and median
Problem-Solving and Data Analysis practice question
The data set 2, 3, 3, 4, 5, 6, 40 gives the number of minutes seven customers waited. Which statement about the mean and median of the data set is true?
- A. The mean is greater than the median, because the value 40 pulls the mean up.Correct
- B. The median is greater than the mean, because the value 40 pulls the median up.
- C. The mean and median are equal, because the data are symmetric.
- D. The median is 5 and the mean is 4.
Answer: A. The mean is greater than the median, because the value 40 pulls the mean up.
Median = 4 (the fourth value). Mean = 63/7 = 9. The outlier 40 lifts the mean but not the median.
Why the other answers are wrong
- B. The median is greater than the mean, because the value 40 pulls the median up.
- Outliers barely affect the median; it stays at 4.
- C. The mean and median are equal, because the data are symmetric.
- The data are strongly skewed by 40.
- D. The median is 5 and the mean is 4.
- The median is 4 and the mean is 9.
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