Problem-Solving and Data AnalysisMediumEffect of an outlier on the mean and median
Problem-Solving and Data Analysis practice question
A data set consists of the ages of 20 people. Nineteen of them are between 30 and 35 years old, and one is 90 years old. Which statement about the data set is true?
- A. The mean is greater than the median.Correct
- B. The mean is less than the median.
- C. The mean and the median are equal.
- D. The median is greater than 40.
Answer: A. The mean is greater than the median.
The median is the middle of the ordered ages, which sits among the nineteen values between 30 and 35. The mean adds every value, so the single age of 90 pulls it upward. A high outlier raises the mean but barely moves the median, so the mean is greater.
Why the other answers are wrong
- B. The mean is less than the median.
- A value far ABOVE the rest drags the mean up, not down. The mean would be less than the median if the outlier were unusually low.
- C. The mean and the median are equal.
- They'd be roughly equal only if the data were symmetric. One value 55 years above the others breaks the symmetry and lifts the mean.
- D. The median is greater than 40.
- Nineteen of the twenty ages are 35 or under, so the middle value is 35 or under. One extreme value can't move the median past 40.
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What is the difference between the mean and the median of this data set?
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