Geometric Mean Practice

The geometric mean of two numbers a and b is the square root of their product, calculated as √(a * b).

The geometric mean of three numbers a, b, and c is the cube root of their product, calculated as (a * b * c)^(1/3).

The geometric mean of n numbers x1, x2, ..., xn is given by (x1 * x2 * ... * xn)^(1/n).

x = √(4 * 16) = √64 = 8.

The arithmetic mean is always greater than or equal to the geometric mean for non-negative numbers, with equality when all numbers are the same.

The geometric mean is used to calculate average rates of return over time, especially when dealing with percentages.

The geometric mean can be used to find the average growth rate of an investment over multiple periods.

Geometric mean = (3 * 6 * 12)^(1/3) = 6.

The geometric mean is preferred when dealing with multiplicative processes or ratios, as it better represents the central tendency.

Geometric mean = (1 * 2 * 3)^(1/3) = 1.817.