Editing Arithmetic mean (section)

==Definition==
The arithmetic mean of a set of observed data is equal to the sum of the numerical values of each observation, divided by the total number of observations. Symbolically, for a data set consisting of the values <math>x_1,\dots,x_n</math>, the arithmetic mean is defined by the formula:

:<math>\bar{x}=\frac{1}{n}\left (\sum_{i=1}^n{x_i}\right)
=\frac{x_1+x_2+\dots+x_n}{n}</math><ref>{{Cite web|last=Weisstein|first=Eric W.|title=Arithmetic Mean|url=https://mathworld.wolfram.com/ArithmeticMean.html|access-date=2020-08-21|website=mathworld.wolfram.com|language=en}}</ref>

(For an explanation of the summation operator, see [[summation]].)

In simpler terms, the formula for the arithmetic mean is:

<math>\frac{\text{Total of all numbers within the data}}{\text{Amount of total numbers within the data}}
</math>

For example, if the monthly salaries of <math>10</math> employees are <math>\{2500,2700,2400,2300,2550,2650,2750,2450,2600,2400\}</math>, then the arithmetic mean is:

:<math>\frac{2500+2700+2400+2300+2550+2650+2750+2450+2600+2400}{10}=2530</math>

If the data set is a [[statistical population]] (i.e., consists of every possible observation and not just a subset of them), then the mean of that population is called the ''[[population mean]]'' and denoted by the [[Greek alphabet|Greek letter]] <math>\mu</math>. If the data set is a [[Sampling (statistics)|statistical sample]] (a subset of the population), it is called the ''[[sample mean]]'' (which for a data set <math>X</math> is denoted as <math>\overline{X}</math>).

The arithmetic mean can be similarly defined for [[Vector (mathematics and physics)|vectors]] in multiple dimensions, not only [[Scalar (mathematics)|scalar]] values; this is often referred to as a [[centroid]]. More generally, because the arithmetic mean is a [[convex combination]] (meaning its coefficients sum to <math>1</math>), it can be defined on a [[convex space]], not only a vector space.