Features of a Set Given Same Value for Maximum and Average

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What else, if anything, can be said if the maximum of a set is equal to the average value in the set? If the average is equal to both the maximum and minimum then all the values are the same, but can anything be said if only the maximum and average are the same?

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For example, if 9 is the maximum of a set, then no value can be higher. If no value can be higher than 9, than all the other value must be ..., if the average is 9.

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calculus