In statistics, dispersion denotes how stretched or squeezed a distribution is, but what is the formal definition? In statistics, dispersion denotes how stretched or squeezed a distribution is, but what is the formal definition by mathematical properties?
 A: There are many measures of dispersion (scatter and other terms).
Some of the most common measures of dispersion include:


*

*Variance (Standard Deviation)

*Range: The range is the difference between the largest and smallest values of a distribution. Not useful if dealing with infinite quantities.  

*Semi-Interquartile Range: If $\displaystyle x_{.25}$ and $x_{.75}$ represent the $25^{th}$ and $75^{th}$ percentile values, the difference $\displaystyle x_{.75} - x_{.25}$ is called the interquartile range and $\displaystyle \frac{1}{2}\left(x_{.75} - x_{.25}\right)$ is the semi-interquartile range.

*Mean Deviation: The Mean Deviation (M.D.) of a random variable X is defined as the expectation of $\left|X -\mu\right|$, that is:


$$M.D.(X) = E\left[|X -\mu|\right] = \sum |X-\mu|f(x) ~~~~\text{(discrete variable)}$$
$$M.D.(X) = E\left[|X -\mu|\right] = \int_{-\infty}^{\infty} |X-\mu|f(x) dx~~~~\text{(continuous variable)}$$
Having said that, there are others too, but hopefully this gets you kick started.
