Problem-Solving and Data AnalysisVery hardComparing mean and median in a skewed set
Problem-Solving and Data Analysis practice question
The salaries at a small company are $40,000 for each of nine employees and $400,000 for the owner. Which statement is true?
- A. The mean salary is $76,000, and the median is $40,000; the mean is pulled up by the owner's salary.Correct
- B. The mean and the median are both $40,000.
- C. The median is $76,000, and the mean is $40,000.
- D. The mean is $220,000.
Answer: A. The mean salary is $76,000, and the median is $40,000; the mean is pulled up by the owner's salary.
Mean: (9 × 40,000 + 400,000)/10 = 760,000/10 = 76,000. Median: with ten values, the middle two are both 40,000. The single high value lifts the mean, not the median.
Why the other answers are wrong
- B. The mean and the median are both $40,000.
- The mean includes the $400,000 and is much higher.
- C. The median is $76,000, and the mean is $40,000.
- Swapped: the median is the typical value, 40,000.
- D. The mean is $220,000.
- $220,000 is the mean of just 40,000 and 400,000, ignoring how many earn each.
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