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.