Arithmetic Mean

Topics: Measure of Central Tendency - Statistics

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(definition)

Let $x_1,\dots ,x_n$ be observations (realisations) of a variable $X$.

The arithmetic mean consists in the sum of all values divided by the amount of values:

$$\mathrm{Mean}(X)=\frac{{\sum }_{i=1}^n{x}_i}{n}=\frac{x_1+\cdots +x_n}{n}$$

It is also possible to calculate the arithmetic mean when our data has weights or is a table of frequencies or is grouped in classes.

Properties §

Let $x_1,\dots ,x_n$ be observations of a variable and let $c$ be a constant. Then:

• $\mathrm{Mean}(cX)=c\mathrm{Mean}(X)$
• $\mathrm{Mean}(X+c)=\mathrm{Mean}(X)+c$