021. The Geometric Mean

The Geometric mean can be used to show percentage changes in a series of positive numbers, and it also represents the average change over time. It has wide application in business and economics (the percentage change in sales, gross national product, etc.).

GM is found by taking the NTh root of the product of N numbers. Thus,

. (3.6)

The Geometric mean will always be less than the arithmetic mean except in the rare case when all the percentage increases are the same. Then the two means are equal.

Example 3.5. The geometric mean of 5, 6, 8, and 12 is

.

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