Geometric Mean

Author

Eric W. Weisstein
June 21, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/GeometricMean.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GeometricMean.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Statistics`DescriptiveStatistics`

Code

MyGeometricMean[l_List]:=(Times@@l)^(1/Length[l])

Examples

Table[Subtract@@Through[{GeometricMean,MyGeometricMean}[Array[x,n]]],{n,10}]

GeometricMean[{(Subscript[x, 1]),(Subscript[x, 2])}]

GeometricMean[{(Subscript[x, 1]),(Subscript[x, 2]),(Subscript[x, 3])}]

Relationship to A and H

With[{n=2},Eliminate[Thread[{G,H,A}==Through[{GeometricMean,HarmonicMean,Mean}[Array[x,n]]]^n],Array[x,n]]
]

Solve[G^2==A H,H]

With[{n=3},Eliminate[Thread[{g,h,a}==Through[{GeometricMean,HarmonicMean,Mean}[Array[x,n]]]^n],Array[x,n]]
]