contraharmonic mean
English
editEtymology
editThe contraharmonic mean of two variables is at the same distance from their arithmetic mean as their harmonic mean but on the opposite side.
Noun
editcontraharmonic mean (plural contraharmonic means)
- (mathematics) A type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, ie.
- The contraharmonic mean of two numbers and is the number such that . Combining the two ratios: . Rotating the proportion 90° clockwise: ; transposing twice to isolate the : . Likewise ; these are both equivalent to the more symmetrical .
Translations
edittype of average
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See also
editReferences
edit- Means, Meaning, and Music: Pythagoras, Archytas, and Plato by Scott Makeig, §The Tetractus of Means