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HarmonicMean

HarmonicMean[list]
gives the harmonic mean of the values in list.
  • For the list , the harmonic mean is given by .
Harmonic mean of symbolic values:
Harmonic mean of columns of a matrix:
Harmonic mean of symbolic values:
In[1]:=
Click for copyable input
Out[1]=
 
Harmonic mean of columns of a matrix:
In[1]:=
Click for copyable input
Out[1]=
Compute results at machine precision:
Obtain results at any precision:
Compute results for a large vector or matrix:
HarmonicMean is the inverse of Mean of the inverse of the data:
HarmonicMean is logarithmically related to GeometricMean for positive values:
For positive data, HarmonicMean[d]≤GeometricMean[d]≤Mean[d]:
Prove the inequality symbolically:
HarmonicMean[Range[n]] is inversely related to HarmonicNumber[n]:
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