Dictionary

harmonic mean en · NOUN

Pronunciation

• (Southern-England) audio

Meanings

1. A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, i.e., H=n/1/x_1+1/x_2+⋯+1/x_n.
   • The harmonic mean of two numbers a and c is the number b such that #123;a-b#92;overa#125;#61;#123;b-c#92;overc#125;. Combining the two ratios: #123;b-c#92;overc#125;#61;#123;(a-b)#43;(b-c)#92;overa#43;c#125;#61;#123;a-c#92;overa#43;c#125;. Rotating the proportion 90° clockwise: #123;c#92;overa#43;c#125;#61;#123;b-c#92;overa-c#125;; transposing twice to isolate the b: b#61;c#43;c#92;left(#123;a-c#92;overa#43;c#125;#92;right). Likewise b#61;a-a#92;left(#123;a-c#92;overa#43;c#125;#92;right); these are both equivalent to the more typical, symmetrical equations: b#61;#123;2ac#92;overa#43;c#125;#61;#123;2#92;over#123;1#92;overa#125;#43;#123;1#92;overc

Forms

Deriveds

contraharmonic mean

Hypernyms

measure of central tendency · Pythagorean mean

Relateds

arithmetic mean · quadratic mean · geometric mean

Translations (18)

fi harmoninen keskiarvo (type of average) · sh harmonijska sredina (type of average) · ja 調和平均 (type of average) · pl średnia harmoniczna (type of average) · de harmonisches Mittel (type of average) · es media armónica (type of average) · tl suwatuhing tamtaman (type of average) · cmn 調和平均數 /调和平均数 (type of average) · id rerata harmonik (type of average) · ru сре́днее гармони́ческое (type of average) · cs harmonický průměr (type of average) · pt média harmônica (type of average) · ko 조화 평균 (type of average) · fr moyenne harmonique (type of average) · hi हरात्मक माध्य (type of average) · pt média harmónica (type of average) · sv harmoniskt medelvärde (type of average) · hu harmonikus közép (type of average)