arithmetic mean

The mean is among the most fundamental tools in statistics for describing the central behavior of a data distribution.

The arithmetic mean is the most common and intuitive form of average. In general form, the arithmetic mean is expressed as:

\[
M_a = \frac{1}{n}\sum_{i=1}^{n} x_i
\]

The geometric mean belongs to the family of power means. In general form, it is expressed as:
\[
M_g = \left( \prod_{i=1}^{n} x_i \right)^{\frac{1}{n}}
\]

This mean is particularly appropriate when averaging rates, ratios, or speeds, such as velocity, cost per unit, or productivity, cases where smaller values exert a stronger influence on the overall balance. In general form, the harmonic mean is expressed as:

\[
M_-1 = \frac{n}{\displaystyle\sum_{i=1}^{n} \frac{1}{x_i}}
\]

The quadratic mean represents the effective magnitude of a set of values, regardless of their sign. In general form, the quadratic mean is expressed as:

\[
M_2 = \sqrt{\frac{1}{n} \sum_{i=1}^{n} x_i^2}
\]