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In the time of Pythagoras there were only three means Bakker (J Stat Edu 11:1, 2003), Brown (Phronesis 20(2):173–184, 1975) and Huffman (Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King. Cambridge University Press, Cambridge, 2005) the arithmetic, the geometric, and third that was called subcontrary, but the “name of which was changed to harmonic by Archytas of Tarentum and Hippasus and their followers, because it manifestly embraced the ratios of what is harmonic and melodic” (Huffman, Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King. Cambridge University Press, Cambridge, 2005, p. 164). The harmonic mean is a measure of location used mainly in particular circumstances—when the data consists of a set of rates, such as prices ($/kilo), speeds (mph) or productivity (output/manhour). lt is defined as the reciprocal of the arithmetic mean of the reciprocals of the values.

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Harmonic Mean

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  • 发表日期：

    2025年

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  • Jasmin Komić

摘要

In the time of Pythagoras there were only three means Bakker (J Stat Edu 11:1, 2003), Brown (Phronesis 20(2):173–184, 1975) and Huffman (Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King. Cambridge University Press, Cambridge, 2005) the arithmetic, the geometric, and third that was called subcontrary, but the “name of which was changed to harmonic by Archytas of Tarentum and Hippasus and their followers, because it manifestly embraced the ratios of what is harmonic and melodic” (Huffman, Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King. Cambridge University Press, Cambridge, 2005, p. 164). The harmonic mean is a measure of location used mainly in particular circumstances—when the data consists of a set of rates, such as prices ($/kilo), speeds (mph) or productivity (output/manhour). lt is defined as the reciprocal of the arithmetic mean of the reciprocals of the values.