Arithmetic Mean
Definition
For $n$ values $x_{1}, x_{2}, \dots, x_{n}$, the following quantity is called their arithmetic mean.
$$ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_{i} = \frac{x_{1} + x_{2} + \dots + x_{n}}{n} $$
Explanation
Since $\sum_{i=1}^{n} x_{i} = n \bar{x} = \sum_{i=1}^{n} \bar{x}$ in the definition, the arithmetic mean is "the number that, when added $n$ times, yields the total sum of the $n$ values". It coincides with the ordinary notion of an average. The number which, when raised to the power $n$, yields the total product of the $n$ values is called the geometric mean.
It is one of the representative measures of a set of values. If the $x_{i}$ are periodic quantities (the field that deals with such data is called directional statistics), their average cannot be represented simply by the arithmetic mean; therefore one defines a separate [mean direction].