Statistical dispersion

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In statistics, statistical dispersion (also called statistical variability or variation) is variability or spread in a variable or a probability distribution. Common examples of measures of statistical dispersion are the variance, standard deviation and interquartile range.

Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.

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Measures of statistical dispersion

A measure of statistical dispersion is a real number that is zero if all the data are identical, and increases as the data becomes more diverse. It cannot be less than zero.

Most measures of dispersion have the same scale as the quantity being measured. In other words, if the measurements have units, such as metres or seconds, the measure of dispersion has the same units. Such measures of dispersion include:

These are frequently used (together with scale factors) as estimators of scale parameters, in which capacity they are called estimates of scale.

All the above measures of statistical dispersion have the useful property that they are location-invariant, as well as linear in scale. So if a random variable X has a dispersion of SX then a linear transformation Y = aX + b for real a and b should have dispersion SY = |a|SX.

Other measures of dispersion are dimensionless (scale-free). In other words, they have no units even if the variable itself has units. These include:

There are other measures of dispersion:

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