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The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers, the geometric mean is defined as.For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is.or example, the geometric mean of 2 and 8 can be calculated as: where is any base of a logarithm (commonly 2, or 10). The right-hand side formula above is generally the preferred alternative for implementation in computer languages.
The geometric mean is a measure of central tendency, just like a median. It is different than the traditional mean (which we sometimes call the arithmetic mean) because it uses multiplication rather than addition to summarize data values. The geometric mean is a useful summary when we expect that changes in the data occur in a relative fashion. Here are some examples where we would expect relative changes: Filters will trap dusts in an amount relative to the amount of air flowing through them. Adjustments in salary are often a percentage amount.