Problem-Solving and Data AnalysisVery hardEffect on the median of changing an extreme value
Problem-Solving and Data Analysis practice question
A data set of 11 values has a median of 30. The largest value in the set is 90. If the largest value is changed to 150 and all other values stay the same, what happens to the median?
- A. It stays 30.Correct
- B. It increases by 60.
- C. It increases, but by less than 60.
- D. It decreases.
Answer: A. It stays 30.
The median is the middle (6th) value once sorted. Making the largest value larger doesn't change which value is in the middle, so the median stays 30.
Why the other answers are wrong
- B. It increases by 60.
- The MEAN would rise by 60/11; the median doesn't depend on the size of extreme values.
- C. It increases, but by less than 60.
- The median doesn't move at all when an extreme value gets more extreme.
- D. It decreases.
- Raising a value can't lower the median.
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