Problem-Solving and Data AnalysisVery hardLargest possible value given a mean and a median
Problem-Solving and Data Analysis practice question
Five positive integers have a mean of 10 and a median of 12. What is the greatest possible value of the largest of the five integers?
Answer: 24
The sum is 50 and the middle value is 12. To make the largest value as big as possible, take the two smallest as 1 and 1 and the fourth as 12, leaving 50 − 26 = 24.
Common wrong answers
- If you answered 12
- 12 is the median.
- If you answered 26
- 26 uses 0 for the two smallest values, which are not positive.
- If you answered 38
- 38 forgets that the fourth value must be at least 12.
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