what is geometric mean

The geometric mean is a type of average that indicates the central tendency of a finite set of real numbers by using the product of their values. It is defined as the nth root of the product of n numbers, where n is the total number of data values. The geometric mean is different from the arithmetic mean, which adds the data values and then divides by the total number of values. The geometric mean is most commonly used when the numbers are restricted to being non-negative or positive, to avoid complications related to negative numbers not having real roots, and to enable the use of logarithms. The geometric mean can be understood in terms of geometry. For example, the geometric mean of two numbers is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a and b. The geometric mean is useful in many fields, including stock indexes and investment portfolios.