## Geometric mean

Geometric mean** ^{1 }**is a representative statistic for the set of products expressed in Eq. 3.

**Geometric mean = (R _{1}*R_{2}*R_{S}*R_{N})^{(1/N)}**

**Equation 3**

Equation 3 states that geometric mean is the N^{th} root of a product. The N^{th} root is **(1/N), **with **N** being the number of terms in the product. The product’s terms are labeled **R _{1}** for the 1

^{st}term,

**R**for the 2

_{2}^{nd }term,

**R**for subsequent terms, and

_{S }**R**for the final term of the series.

_{N}The calculation of compound annual growth rate (CAGR) is a special case of the geometric mean in which Eq. 3 takes the special form **(V _{1}/V_{0}* V_{2}/V_{1} * V_{N}/V_{(N-1)})^{(1/N)}**. The latter formula factors out to the

**(V**term used in Eq. 1.

_{N}/V_{0})^{(1/N) }## Arithmetic mean

Arithmetic mean** ^{1 }**is a statistic for the set of sums expressed in Eq. 4.

**Arithmetic mean = (V _{1}+V_{2}+V_{N})/N**

**Equation 4**

According to Eq. 4, arithmetic mean is the quotient of a sum. The numerator is a sum of values and the denominator is the number of values in the sum.

Copyright © 2011 Douglas R Knight

## References

1. Geometric mean. Copyright © 2011 Investopedia ULC. http://www.investopedia.com/terms/g/geometricmean.asp#axzz1ceLXsjvF.