Problem-Solving and Data AnalysisEasy–MediumMean versus median with an outlier
Problem-Solving and Data Analysis practice question
For the data set 2, 3, 4, 5, 26, which statement is true?
- A. The mean is greater than the median, because the unusually large value 26 pulls the mean up.Correct
- B. The median is greater than the mean, because the median counts the largest value more heavily.
- C. The mean and the median are equal, because the data set has an odd number of values.
- D. The mean is 4, the middle value of the set.
Answer: A. The mean is greater than the median, because the unusually large value 26 pulls the mean up.
Median: the middle value, 4. Mean: 40/5 = 8. The outlier 26 lifts the mean well above the median.
Why the other answers are wrong
- B. The median is greater than the mean, because the median counts the largest value more heavily.
- The median ignores how large the extreme value is; it's the mean that's affected.
- C. The mean and the median are equal, because the data set has an odd number of values.
- An odd count only makes the median easy to find; it doesn't make it equal the mean.
- D. The mean is 4, the middle value of the set.
- 4 is the MEDIAN. The mean is 8.
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