> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/990-misc/810-statistics/arithmetic-mean.md).

# Mathematical Concepts

## Geometric Mean

The **Geometric Mean** (GM) is an average that indicates the central tendency or typical value of a set of numbers by using the product of their values.

The geometric mean is defined as the $$n^{th}$$ root of the product of $$n$$ numbers.

For a set of numbers $$x1, x2, \dots, xn$$, GM is defined as:

$$
\displaystyle
\left(\prod \_{i=1} ^{n} {x\_i}
\right)^{1/n} =\ \sqrt\[n] {x\_1 \ x\_2 \cdots x\_n }
$$

Examples:

* the geometric mean of two numbers is the square root of their product:    

  $$\sqrt{2\cdot 8} = 4$$
* the geometric mean of 3 numbers is the cube root of their product:    

  $${{\sqrt\[{3}]{4\cdot 1\cdot 1/32}}=1/2}$$

## Arithmetic Mean

The **Arithmetic Mean** (AM) is an average that indicates the central tendency or typical value of a set of numbers by using the sum of their values.