Geometric mean

The geometric mean ofsetpositive datadefined asproduct allmembers ofset, raised topower equal toreciprocal ofnumbermembers. The geometric meanusefuldetermine "average factors". For example, ifstock rose 10% infirst year, 20% insecond yearfell 15% inthird year, then we computegeometric mean offactors 1.10, 1.200.85 as (1.10 × 1.20 × 0.85)^1/3 = 1.0391...we conclude thatstock rose on average 3.91 percent per year.

The geometric mean ofdata setalways smaller than or equal toset's arithmetic mean (the two meansequal ifonly if all members ofdata setequal). This allowsdefinition ofarithmetic-geometric mean,mixture oftwo which always liesbetween.

See also: average, arithmetic mean, arithmetic-geometric mean, harmonic mean, geometric standard deviation.