Harmonic and geometric means

For positive values, the harmonic mean H = n/∑(1/x) and the geometric mean G = (∏x) raised to the power of 1/n ^1/n. H is useful for averaging rates over equal amounts, such as speeds over equal distances. G is useful for multiplicative growth factors. For positive observations, H ≤ G ≤ arithmetic mean, with equality when all observations are equal. Do not use G directly on negative growth percentages; convert percentages to positive growth factors first.