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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 applies only to numbers of the same sign. 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.he geometric mean of a data set is less than the data set's arithmetic mean unless all members of the data set are equal, in which case the geometric and arithmetic means are equal.