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Answer» What is Geometric Mean mean? In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers x1, x2, ..., xn, the geometric mean is defined as ( ∏ i = 1 n x i ) 1 n = x 1 x 2 ⋯ x n n {\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}} For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, 2 ⋅ 8 = 4 {\displaystyle {\sqrt {2\cdot 8}}=4} . As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2, that is, 4 ⋅ 1 ⋅ 1 / 32 3 = 1 / 2 {\displaystyle {\sqrt[{3}]{4\cdot 1\cdot 1/32}}=1/2} . The geometric mean applies only to positive numbers. The geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as a set of growth figures: values of the human population or interest rates of a financial investment over time. The geometric mean can be understood in terms of geometry. The geometric mean of two numbers, reference
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