How is the geometric mean calculated?

The geometric mean is calculated by taking the nth root of the product of n values. This method is particularly useful when dealing with datasets that have values with differing scales or when the values represent growth rates, ratios, or percentages. The formula can be articulated as follows: if you have a set of n numbers, x1, x2, ..., xn, the geometric mean is expressed as:

Geometric Mean = (x1 * x2 * ... * xn)^(1/n)

This approach effectively captures the central tendency of multiplicative processes, ensuring that extreme values have a balanced effect on the mean.

In contrast, the other methods involve different types of calculation. Simply averaging the values would provide the arithmetic mean, while summing the values and dividing by n also calculates the arithmetic mean. Finding the square of the product of the values does not correspond with any typical mean calculation method. Therefore, the correct approach is the one that accurately reflects the nature of the geometric mean through the product and nth root.