Description:
The geometric mean only applies to positive numbers. It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.
Any time you have a number of factors contributing to a product, and you want to find the "average" factor, the answer is the geometric mean. The example of interest rates is probably the application most used in everyday life.
Example:
Suppose that I’m 30% richer than last year, but last year I was 20% richer than the year before… what is the average growth? Well, my current wealth is 1.3 * 1.2 * w if w is my wealth two years ago. I can expect that if t is the average growth factor over the last two years, then my current wealth is t * t * w. Setting t = 1.25 is the wrong answer. In such a case, choosing t = sqrt(1.3 * 1.2) solves the problem.
Sources:
http://www.daniel-lemire.com/blog/archives/2006/04/21/when-use-the-geometric-mean/
http://en.wikipedia.org/wiki/Geometric_mean
http://www.math.toronto.edu/mathnet/questionCorner/geomean.html
