2001 AIME I Problems/Problem 2
Contents
Problem
A finite set of distinct real numbers has the following properties: the mean of is less than the mean of , and the mean of is more than the mean of . Find the mean of .
Solution
Let be the mean of . Let be the number of elements in . Then, the given tells us that and . Subtracting, we have We plug that into our very first formula, and get:
Solution 2
Since this is a weighted average problem, the mean of is as far from as it is from Thus, the mean of is .
See Also
2001 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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All AIME Problems and Solutions |
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