Geometric Mean

The geometric mean, also known as the mean proportional, is a mean or average that indicates the central tendency of a finite collection of positive real numbers by using the product of their values rather than their sum, as the arithmetic mean does. For a set of numbers it equals the nth root of their product, and for two numbers it is simply the square root of their product. It is especially useful for averaging ratios such as growth rates: for a sequence of annual investment returns of plus ten percent, minus twelve percent, plus ninety percent, minus thirty percent and plus twenty five percent, the geometric mean of the growth ratios gives an average annual growth of about 9.98 percent, while the arithmetic mean of the same figures misleadingly suggests growth of 16.6 percent a year.