Difference between revisions of "Geometric mean"

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The '''Geometric Mean''' is the nth root of the product of n numbers. It is analogous to the [[Arithmetic Mean]], except with products. For example, if I wanted to find the Geometric Mean of 2, 4, and 8, I would compute the cube root of 2*4*8=64, which is 4.
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Given a set of ''n'' numbers, the '''Geometric Mean''' is the ''nth'' root of the product of the numbers. It is analogous to the [[Arithmetic Mean]], except with products.  
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== Examples ==
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Find the geometric mean of the numbers <math>x_1, x_2, x_3, x_4 ... x_n</math>
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We want the nth root of the product of the n numbers. There are n numbers so our geometric mean would be <math>\sqrt[n]{x_1 x_2 x_3 x_4 ... x_n}</math>
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Find the geometric mean of the numbers 6, 4, 1 and 2.
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There are 4 numbers, so we want the 4th root. The numbers' product is 48, so our answer is <math>\sqrt[4]{48}=2\sqrt[4]{3}</math>
  
 
The Geometric Mean is a component of the well-known [[Arithmetic Mean-Geometric Mean]] [[Inequality]].
 
The Geometric Mean is a component of the well-known [[Arithmetic Mean-Geometric Mean]] [[Inequality]].
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== Practice Problems ==
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== See Also ==
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*[[Arithmetic Mean]]
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*[[AM-GM]]

Revision as of 11:25, 22 June 2006

Given a set of n numbers, the Geometric Mean is the nth root of the product of the numbers. It is analogous to the Arithmetic Mean, except with products.

Examples

Find the geometric mean of the numbers $x_1, x_2, x_3, x_4 ... x_n$ We want the nth root of the product of the n numbers. There are n numbers so our geometric mean would be $\sqrt[n]{x_1 x_2 x_3 x_4 ... x_n}$


Find the geometric mean of the numbers 6, 4, 1 and 2. There are 4 numbers, so we want the 4th root. The numbers' product is 48, so our answer is $\sqrt[4]{48}=2\sqrt[4]{3}$

The Geometric Mean is a component of the well-known Arithmetic Mean-Geometric Mean Inequality.

Practice Problems

See Also

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