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, $H={n \over {1 \over x_{1}}+{1 \over x_{2}}+\cdots {1 \over x_{n}}}$

   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), 调和平均数 (tiáohé píngjūnshù)

• Czech: harmonický průměr m
• Finnish: harmoninen keskiarvo
• French: moyenne harmonique
• German: harmonisches Mittel n
• Hungarian: harmonikus közép
• Japanese: 調和平均 (ja) (chōwaheikin)
• (deprecated template usage) {{trans-mid}}
• 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