## geometric mean

### the mean of n numbers expressed as the n-th root of their product

Geometric mean is a type of average that helps in determining the central tendency of a given set of numbers by taking the nth root of the product of n numbers. It is essentially the square root of the product of two or more numbers.

To calculate the geometric mean of a set of numbers, follow these steps:

1. Multiply all the numbers in the set together.

2. Take the nth root of the product, where n represents the number of elements in the set.

For example, suppose you have a set of three numbers: 2, 5, and 10. First, multiply the three numbers together: 2 x 5 x 10 = 100. Next, take the cube root (since there are three numbers in the set) of the product: cube root of 100 = 4.64. Therefore, the geometric mean of the set 2, 5, and 10 is 4.64.

The geometric mean is often used in finance and investments to measure the average rate of return over a period of time. It is also used in statistical analysis to compare different sets of data. Keep in mind that the geometric mean is always equal to or less than the arithmetic mean (regular average) of the same set of numbers.

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