Problem-Solving and Data AnalysisHardMedian unchanged by balanced extremes
Problem-Solving and Data Analysis practice question
The data set 4, 6, 8, 10, 12 has a median of 8. The values 1 and 20 are added to the data set. What is the median of the new data set?
Answer: 8
Ordered, the new set is 1, 4, 6, 8, 10, 12, 20. With seven values, the median is the fourth: still 8. One value went below and one above, so the middle didn't move.
Common wrong answers
- If you answered 6
- 6 would be the median if only the 1 had been added; the 20 balances it.
- If you answered 10.5
- 10.5 is (1 + 20)/2, the average of the two added values, not the median.
- If you answered 8.71
- 8.71 is the new MEAN (61/7). The median is the middle value, 8.
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