Geometric Mean

The geometric mean is a type of average that indicates the central tendency of a set of numbers by using the product of their values. The geometric mean is defined as the nth root of the product of n numbers, which is equivalent to exp(the sum of the logarithms of the numbers divided by the number of numbers). To calculate it, each number in the set is replaced with its natural logarithm. The sum of these logarithms is then divided by the quantity of numbers in the set. The exponential of this result gives the geometric mean.

The geometric mean is useful when comparing different items with very different ranges, or when the values are not normally distributed, such as in the case of rates, ratios, or index numbers. It is also relevant in finance, for instance, to calculate average growth rates over time or the return on investment for various financial instruments.