1.NounA 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
2
×
4
×
1
3
{\displaystyle {\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
)
=
x
+
y
2
{\displaystyle A(x,y)={x+y \over 2}}
,
H
(
x
,
y
)
=
2
x
y
x
+
y
{\displaystyle H(x,y)={2xy \over x+y}}
, and
G
(
x
,
y
)
=
x
y
{\displaystyle G(x,y)={\sqrt {xy}}}
, then
G
(
A
(
x
,
y
)
,
H
(
x
,
y
)
)
=
x
+
y
2
⋅
2
x
y
x
+
y
=
x
y
=
G
(
x
,
y
)
{\displaystyle G(A(x,y),H(x,y))={\sqrt {{x+y \over 2}\cdot {2xy \over x+y}}}={\sqrt {xy}}=G(x,y)}
."