Problem-Solving and Data AnalysisVery hardChange that leaves the median alone
Problem-Solving and Data Analysis practice question
The data set 5, 8, 9, 12, 15 has a median of 9. Which of the following changes to the data set would NOT change the median?
- A. Replacing the 15 with 100Correct
- B. Replacing the 9 with 11
- C. Removing the 5
- D. Adding the value 20
Answer: A. Replacing the 15 with 100
The median is the middle value. Making the largest value even larger leaves the order — and the middle — unchanged: 5, 8, 9, 12, 100 still has median 9.
Why the other answers are wrong
- B. Replacing the 9 with 11
- The middle value becomes 11.
- C. Removing the 5
- With four values (8, 9, 12, 15) the median is (9 + 12)/2 = 10.5.
- D. Adding the value 20
- With six values (5, 8, 9, 12, 15, 20) the median is (9 + 12)/2 = 10.5.
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