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Average or arithmetic mean equals the sum of all values of a set of numbers over the number of values.

So to get the sum of all values you take the mean and multiply it by the number of values.

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Mean:

(1) A quantity corresponding to one of possibly several different definitions of the "average" of a set of values. Examples include the arithmetic mean and the geometric mean.

(2) The arithmetic mean (a.k.a. average).

If you want the arithmetic mean than the sum of the values will be the product of the arithmetic mean and the number of values.

I don't believe you can calculate the sum of the values with only the the number of values and the geometric mean or any of the other variations of the mean.

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