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Mathematica > Data Manipulation > Statistical Data Analysis > Descriptive Statistics > GeometricMean >

BUILT-IN MATHEMATICA SYMBOL

GeometricMean

GeometricMean[list]
gives the geometric mean of the values in list.

Geometric mean of a list:

Geometric mean of columns of a matrix:

Geometric mean of a list:

Out[1]=

Geometric mean of columns of a matrix:

Out[1]=

Compute results at machine precision:

Obtain results at any precision:

Compute results for a large vector or matrix:

Compute results for a SparseArray:

GeometricMean is logarithmically related to Mean for positive values:

GeometricMean is logarithmically related to HarmonicMean for positive values:

For positive data, HarmonicMean[d]≤GeometricMean[d]≤Mean[d]:

Prove the inequality symbolically: