Geometric mean, Arithmetic mean

Geometric mean

Geometric mean1 is a representative statistic for the set of products expressed in Eq. 3.

Geometric mean = (R1*R2*RS*RN)(1/N)

Equation 3

Equation 3 states that geometric mean is the Nth root of a product.   The Nth root is (1/N), with N being the number of terms in the product.  The product’s terms are labeled   R1 for the 1st term, R2 for the 2nd term, RS for subsequent terms, and RN 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 * VN/V(N-1))(1/N).  The latter formula factors out to the (VN/V0)(1/N) term used in Eq. 1.

Arithmetic mean

Arithmetic mean1 is a statistic for the set of sums expressed in Eq. 4.

Arithmetic mean = (V1+V2+VN)/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.

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