Small Trades Journal

Geometric mean

Geometric mean¹ is a representative statistic for the set of products expressed in Eq. 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   R₁ for the 1^st term, R₂ for the 2^nd term, R_S for subsequent terms, and R_N for the final term of the series.

The calculation of compound annual growth rate (CAGR) is a special case of the geometric mean in which Eq. 3 takes the special form (V₁/V₀* V₂/V₁ * V_N/V_(N-1))^(1/N).  The latter formula factors out to the (V_N/V₀)^(1/N) term used in Eq. 1.

Arithmetic mean

Arithmetic mean¹ is a statistic for the set of sums expressed in Eq. 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.

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