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How can I calculate max value or all possible and relevant maximum values, if I know number of records, minimal value and average value of all records?

For example: Number of records (persons): 92 Minimal increase: 20€ Average increase: 33€ Max increase for person: ?

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up vote 3 down vote accepted

You cannot calculate an exact maximum with that information, but you can put wide bounds on it.

The highst possible maximum will be $33 + \frac{91}{1}\times(33-20) = 1034$, happening when all but one of the values are at the minimum

The lowest possible maximum will be $33 + \frac{1}{91}\times(33-20) =33.142857\ldots$, happening when all but one of the values are at the maximum

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