Mean Deviation

Topics: Measure of Dispersion - Statistics

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(definition)

Let $x_1,\dots ,x_n$ be observations of a variable $X$. We define the mean deviation of $X$ as:

$$\mathrm{Dm}(X)=\frac{1}{n}\sum _{i=1}^n\left|x_i-\overline{X}\right|$$

…where $\overline{X}$ is the weighted mean of $X$.

Properties §

• $\mathrm{Dm}(x+c)=\mathrm{Dm}(x)$
• $\mathrm{Dm}(aX)=|a|\mathrm{Dm}(x)$