# harmonic mean

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## harmonic mean

n.
The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.

## harmonic mean

n
(Mathematics) the reciprocal of the arithmetic mean of the reciprocals of a set of specified numbers: the harmonic mean of 2, 3, and 4 is 3( + + )–1 = 3
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## harmon′ic mean′

n.
the statistical mean obtained by taking the reciprocal of the arithmetic mean of the reciprocals of a set of nonzero numbers.
[1880–85]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 harmonic mean - the mean of n numbers expressed as the reciprocal of the arithmetic mean of the reciprocals of the numbersstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parametersmean, mean value - an average of n numbers computed by adding some function of the numbers and dividing by some function of n
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
harmonický průměr
harmonisches Mittel
moyenne harmonique
harmonijska sredina
średnia harmoniczna
harmoniskt medelvärde
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References in periodicals archive ?
Highest genotypic variance was estimated for tolerance index (TI; 184009.6) followed by yield under normal conditions (Yp; 154757.4), yield under drought-stressed conditions (Ys; 147796.6), harmonic mean (HM; 111168.3), geometric mean productivity (GMP; 107787.7) and mean productivity (MP; 105274.6).
In addition, RPGV for processed coffee yield was usIn addition, the harmonic mean of the genotypic values was used to select genotypes with superior genetic value and lower variation between harvests.
The harmonic mean for the cattle egret (37.92 hours, 20 mg/kg) is longer than that for the helmeted guineafowl (29 hours, 10 mg/ kg) (12) and the American black duck (32 hours, 10 mg/kg), (9) and shorter than that for the American flamingo (39.9 hours, 10 mg/kg) (10) and red-tailed hawk (50 hours, 20 mg/kg).
Harmonic mean is the reciprocal of the arithmetic mean of reciprocal which is a conservative average to be used to provide for aggregation lying between the max and min operators and is widely used as a tool to aggregate central tendency data which is usually expressed in exact numerical values .
Harmonic mean represents the ratio of the average of coverage to the average potency of the input.
[H.sub.exp] and [H.sub.p] are called multiplicative harmonic mean and pharmonic mean, respectively.
Chu, "An optimal double inequality among the oneparameter, arithmetic and harmonic means," Revue d'Analyse Numerique et de Theorie de l'Approximation, vol.
Results from Table 3 and Table 4 show that calculated arithmetic mean [bar.[h.sub.i]/h] and harmonic mean H of ratios [bar.[h.sub.i]/h] for individual anthropological measures [h.sub.i] in relation to the standing height h are the same for all age groups and for all sample, with minor deviations.
Fuzzy harmonic mean operators, International Journal of Intelligent Systems 24: 152-172 http://dx.doi.org/10.1002/int.20330
[E.sub.-1, -2](a, b) = 2ab/a + b, is the Harmonic mean;
The section following this one extends the analysis to the harmonic mean, followed by the section with illustrations that compare estimates across the four measures of elasticity: isoelastic, arithmetic, geometric, and harmonic.

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