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Date: 31-8-2019
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Date: 19-7-2019
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Date: 12-9-2019
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The geometric mean of a sequence is defined by
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(1) |
Thus,
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(2) |
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(3) |
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
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(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
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(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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