geometric mean

English

Noun

geometric mean (plural geometric means)

1. (mathematics) A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values.

   The geometric mean of 2, 4 and 1 is $\sqrt[3]{2\times 4\times 1}$ = 2

   The geometric mean of the arithmetic mean and the harmonic mean is the geometric mean. In symbols: if $A(x,y)=\frac{x+y}{2}$, $H(x,y)=\frac{2xy}{x+y}$, and $G(x,y)=\sqrt{xy}$, then $G(A(x,y),H(x,y))=\sqrt{\frac{x+y}{2}\cdot \frac{2xy}{x+y}}=\sqrt{xy}=G(x,y)$.

Hypernyms

• measure of central tendency
• Pythagorean mean

Coordinate terms

• arithmetic mean
• harmonic mean
• quadratic mean

Translations

measure of central tendency

• Armenian: երկրաչափական միջին (erkračʻapʻakan miǰin)
• Chinese:

  Mandarin: 幾何平均數 / 几何平均数 (jǐhé píngjūnshù), 几何中项

• Czech: geometrický průměr m
• Estonian: geomeetriline keskmine
• Finnish: geometrinen keskiarvo (fi), keskiverto (fi)
• French: moyenne géométrique (fr)
• German: geometrisches Mittel n
• Hungarian: mértani közép (hu)
• Japanese: 幾何平均 (ja)
• Korean: 기하 평균 (giha pyeonggyun)
• Polish: średnia geometryczna f
• Romanian: medie geometrică (ro) f
• Russian: сре́днее геометри́ческое (ru) n (srédneje geometríčeskoje)
• Serbo-Croatian: geometrijska sredina f
• Spanish: media geométrica f
• Tagalog: sukgising tamtaman