Problem-Solving and Data AnalysisMediumMedian of an unordered data set with an even count
Problem-Solving and Data Analysis practice question
A soccer team scored 2, 5, 1, 3, 4, and 5 goals in its six matches this season. What is the median number of goals scored per match?
Answer: 3.5 or 7/2
First put the values in order: 1, 2, 3, 4, 5, 5. With six values there are two middle ones — the third and fourth, 3 and 4 — and the median is their average: (3 + 4)/2 = 3.5.
Common wrong answers
- If you answered 3
- 3 is the lower of the two middle values. With an even number of values the median is the AVERAGE of the two in the middle: (3 + 4)/2 = 3.5.
- If you answered 4
- 4 is the upper of the two middle values. Average it with the lower one, 3, to get the median 3.5.
- If you answered 5
- 5 is the mode — the value that appears most often. The median is the middle of the ordered list.
- If you answered 3.33
- 3.33 is the mean, 20/6. The median is found by ordering the values and taking the middle.
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What is the difference between the mean and the median of this data set?
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