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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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    $\begingroup$ If the maximum and average (arithmetic mean) of a finite set are the same, then the minimum must also be the same. $\endgroup$ – Omnomnomnom Jul 9 '14 at 22:10
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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.

greetings,

calculus

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