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# geometric mean

The geometric mean of a set of positive values is determined by taking the $$n$$th root of the product of the values, where $$n$$ is the number (count) of the values. For example, the geometric mean of the numbers 9, 14, and 31 is given by

$\sqrt[3]{(9\times 14\times 31)}\approx 15.75$.

The geometric mean is useful when we would like to know the average value of factors in a product, for example when calculating an average rate of return on an investment over a period when the rates have taken on several different values.

We can give the geometric mean of two values a physical interpretation by thinking of the values as the side lengths of a rectangle. The geometric mean of the values is then the side-length of a square having the same area.

Figure 1: Finding a Square of Equal Area

Citation Info

• [MLA] “geometric mean.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 18 Feb 2014. Web. 18 Feb 2014. <http://platonicrealms.com/>
• [APA] geometric mean (18 Feb 2014). Retrieved 18 Feb 2014 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/geometric-mean/

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