Inequality of Arithmetic and Geometric Means - Background

Background

The arithmetic mean, or less precisely the average, of a list of n numbers x1, x2, . . ., xn is the sum of the numbers divided by n:

The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:

If x1, x2, . . ., xn > 0, this is equal to the exponential of the arithmetic mean of the natural logarithms of the numbers:

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