The geometric mean, sometimes also called geometric average, is an average calculated by multiplying a set of positive values and taking the nth root, where n is the number of values.

The geometric mean is used to minimize the effects of extreme values; for instance, when averaging growth rates.

--- Source: Eurostat

Geometric mean requires that all numbers are > 0.

There are two formula:

1. For N +ve numbers a1, a2, ... aN, GeoMean = Nth root of (a1 ×ばつ a2 ×ばつ ... aN).
2. For N +ve numbers a1, a2, ... aN, GeoMean = exp(sum(ln(a1)), ln(a2), ... ĺn(aN)) / N).

--- Source: Wikipedia

Note that formula 1 could overflow easily, so formula 2 seems the best algorithm.

E.g.:

function GeoMean(const A: array of Double): Double;
begin
 Assert(Length(A) > 0); // replace with exception
 var SumOfLogs: Double := 0.0;
 for var D in A do
 begin
 if Sign(D) <> PositiveValue then
 raise EArgumentOutOfRangeException.Create('Non positive value passed to GeoMean');
 SumOfLogs := SumOfLogs + Ln(A);
 end;
 Result := Exp(SumOfLogs / Length(A));
end;

This function was extracted from issue #16