Problem-Solving and Data AnalysisVery hardLargest value from mean, median and mode
Problem-Solving and Data Analysis practice question
A list of five positive integers has a mean of 6, a median of 5, and a single mode of 3, which appears exactly twice. What is the largest possible value in the list?
Answer: 13
The sum is 30 and the middle value is 5. The two smallest values are 3 and 3, so the two largest add to 19. They must be different from each other and greater than 5 (or 5 would also appear twice), so the smallest choice for the fourth value is 6, leaving 13.
Common wrong answers
- If you answered 14
- 14 would need the fourth value to be 5, making 5 a second mode.
- If you answered 19
- 19 is the sum of the two largest values.
- If you answered 30
- 30 is the sum of the whole list.
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