harmonic mean

harmonic mean

English

Noun

harmonic mean (plural harmonic means)

1. (mathematics) A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie, ${\\displaystyle H={n \\over {1 \\over x_{1}}+{1 \\over x_{2}}+\\cdots +{1 \\over x_{n}}}}$

   If a_n and b_n denote the perimeters of inscribed and circumscribed regular n-gons, respectively, along some circle then the harmonic mean and geometric mean of those two perimeters yield the perimeters of the inscribed and circumscribed regular 2n-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)

Hypernyms

• (statistics): measure of central tendency

Translations

type of average

Chinese: Mandarin: 調和平均數／调和平均数 (tiáohé píngjūnshù) Czech: harmonický průměr m Finnish: harmoninen keskiarvo French: moyenne harmonique German: harmonisches Mittel n Hungarian: harmonikus közép Indonesian: rerata harmonik Japanese: 調和平均 (ja) (chōwaheikin) Korean: 조화 평균 (johwa pyeonggyun) Polish: średnia harmoniczna f Portuguese: média harmónica f (Portugal), média harmônica f (Brazil) Russian: сре́днее гармони́ческое n (srédneje garmoníčeskoje) Serbo-Croatian: harmonijska sredina f Spanish: media armónica f Swedish: harmoniskt medelvärde (sv) n Tagalog: suwatuhing tamtaman

See also

• arithmetic mean
• contraharmonic mean
• geometric mean
• quadratic mean