HarmonicMean
HarmonicMean[list]
gives the harmonic mean of the values in list.
Details

- For the list {x1,x2,…,xn}, the harmonic mean is given by
.
- HarmonicMean handles both numerical and symbolic data.
- HarmonicMean[{{x1,y1,…},{x2,y2,…},…}] gives {HarmonicMean[{x1,x2,…}],HarmonicMean[{y1,y2,…}]}.
Examples
open allclose allScope (9)
Exact input yields exact output:
Approximate input yields approximate output:
HarmonicMean for a matrix gives columnwise means:
SparseArray data can be used just like dense arrays:
Find the harmonic mean of WeightedData:
Find the harmonic mean of EventData:
Find the harmonic mean of a TimeSeries:
Generalizations & Extensions (1)
Compute results for a SparseArray:
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]:
Text
Wolfram Research (2007), HarmonicMean, Wolfram Language function, https://reference.wolfram.com/language/ref/HarmonicMean.html.
CMS
Wolfram Language. 2007. "HarmonicMean." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/HarmonicMean.html.
APA
Wolfram Language. (2007). HarmonicMean. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HarmonicMean.html