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DISPERSION
This is also called the statistical variability or variation which can be defined as the variability or spread in a variable or a probability distribution and the common examples of measures of statistical dispersion are the variance and standard deviation as well as the interquartile range.
It is used with location and when used together they are the most used properties of distributions.
It is a nonnegative real number that is zero and if all the data are the same and this increases as the data become more diverse and most measures of dispersion have the same scale as the quantity being measured.
If the measurements have units of measurement such as meters or seconds, then the measure of dispersion has the same units and such measures of dispersion include the standard deviation and interquartile range as well as the inter-decile range and the range.
It also includes the measures like Mean difference and median absolute deviation as well as the average absolute deviation and the distance standard deviation.
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These are frequently used together with a scale factor as an estimator in which capacity they are called estimates of scale b and the robust measures of scale are those unaffected by a small number of outliers.
All the measures of these have the useful property that they are location-invariant and if a random variable X has a dispersion of SX then a linear transformationY=a X+b for real number a and b should have dispersion SY=|a|SX.
Other measures are dimensionless which does have no units even if the variable itself has units which include the coefficient of variation and quartile coefficient of dispersion. These are also measures such as variance which is the square of the standard deviation and it is location-invariant but not linear in scale.
The variance-to-mean ratio is mostly used for count data when these terms are used if the ratio is dimensionless.
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Some measures have specialized purposes, among them are the Allan variance as well as the Hadamard variance. For the categorical variable, it is less common to measure dispersion by a single number and a measure that does so is the discrete information entropy.
