Geometric Mean
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
29-6-2019
1744
Geometric Mean
The geometric mean of a sequence ![<span style=]()
{a_i}_(i=1)^n" src="http://mathworld.wolfram.com/images/equations/GeometricMean/Inline1.gif" style="height:16px; width:38px" /> is defined by
 |
(1)
|
Thus,
and so on.
The geometric mean of a list of numbers may be computed using GeometricMean[list] in the Wolfram Language package DescriptiveStatistics` .
For 
, the geometric mean is related to the arithmetic mean 
and harmonic mean 
by
 |
(4)
|
(Havil 2003, p. 120).
The geometric mean is the special case 
of the power mean and is one of the Pythagorean means.
Hoehn and Niven (1985) show that
 |
(5)
|
for any positive constant 
.
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 10, 1972.
Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, pp. 119-121, 2003.
Hoehn, L. and Niven, I. "Averages on the Move." Math. Mag. 58, 151-156, 1985.
Kenney, J. F. and Keeping, E. S. "Geometric Mean." §4.10 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 54-55, 1962.
Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 602, 1995.
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