Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Data Manipulation > Statistical Data Analysis > Descriptive Statistics > HarmonicMean >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Descriptive Statistics > HarmonicMean >
BUILT-IN MATHEMATICA SYMBOLTutorials »|See Also »|More About »

HarmonicMean

HarmonicMean[list]
gives the harmonic mean of the values in list.
MORE INFORMATION
  • For the list , the harmonic mean is given by .
EXAMPLESCLOSE ALL
Basic Examples   (2)
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]=
Scope   (3)
Compute results at machine precision:
Obtain results at any precision:
Compute results for a large vector or matrix:
Properties & Relations   (4)
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]:
New in 6
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF