gives the contraharmonic mean of the values in list.


gives the order p Lehmer contraharmonic mean.


  • For the list {x1,x2,,xn}, the contraharmonic mean is given by .
  • The order p Lehmer mean is given by .
  • ContraharmonicMean handles both numerical and symbolic data.
  • ContraharmonicMean[{{x1,y1,},{x2,y2,},}] gives {ContraharmonicMean[{x1,x2,}],ContraharmonicMean[{y1,y2,}]}.


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Basic Examples  (2)

Symbolic values:

Means of each column:

Scope  (9)

Exact input yields exact output:

Approximate input yields approximate output:

ContraharmonicMean for a matrix gives columnwise means:

Works with large arrays:

SparseArray data can be used just like dense arrays:

Find the contraharmonic mean of WeightedData:

Find the contraharmonic mean of EventData:

Find the contraharmonic mean of a TimeSeries:

Find the contraharmonic mean for data involving quantities:

Properties & Relations  (2)

The contraharmonic mean is a quotient of two means:

The geometric mean of the arithmetic and contraharmonic means is the root mean square:

Introduced in 2008