# Geometric Mean

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## Definition of 'Geometric Mean'

The geometric mean is a type of average that is calculated by taking the nth root of the product of n numbers. It is often used in finance to measure the growth of an investment over time.

The geometric mean is different from the arithmetic mean, which is calculated by adding the numbers together and dividing by the number of numbers. The arithmetic mean is often used to measure the average of a set of data, while the geometric mean is used to measure the growth rate of an investment.

The geometric mean is often used in finance because it takes into account the compounding effect of interest. When an investment earns interest, the interest is added to the principal and then earns interest itself. This compounding effect can lead to significant growth over time. The geometric mean takes into account this compounding effect and provides a more accurate measure of the growth of an investment.

The geometric mean can be calculated using the following formula:

```
G = (a1 * a2 * ... * an)^(1/n)
```

where:

* G is the geometric mean
* a1, a2, ..., an are the n numbers in the set
* n is the number of numbers in the set

For example, if you have the following set of numbers: 1, 2, 3, 4, 5, the geometric mean would be calculated as follows:

```
G = (1 * 2 * 3 * 4 * 5)^(1/5) = 3.16227766
```

The geometric mean is often used in finance to measure the growth of an investment over time. It is a more accurate measure of growth than the arithmetic mean because it takes into account the compounding effect of interest.

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