# 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:   &#x20;

    $$\sqrt{2\cdot 8} = 4$$
*   the geometric mean of 3 numbers is the cube root of their product:   &#x20;

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

## 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.
