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A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion.
The above definition indicates, in the one-dimensional case, that if is increased, the probability density or mass function shifts rigidly to the right, maintaining its exact shape. A location parameter can also be found in families having more than one parameter, such as location–scale families. In this case, the probability density function ...
a measure of location, or central tendency, such as the arithmetic mean; a measure of statistical dispersion like the standard mean absolute deviation; a measure of the shape of the distribution like skewness or kurtosis; if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution. [1] Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s. [2] The most common measures of central tendency are the arithmetic mean, the median, and ...
Some measures that are commonly used to describe a data set are measures of central tendency and measures of variability or dispersion. Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness ...
The measures of statistical dispersion derived from absolute deviation characterize various measures of central tendency as minimizing dispersion: The median is the measure of central tendency most associated with the absolute deviation. Some location parameters can be compared as follows: L 2 norm statistics: the mean minimizes the mean ...
Dispersion captures the degree to which points in a point set are separated from each other. For most applications, spatial dispersion should be quantified in a way that is invariant to rotations and reflections. Several simple measures of spatial dispersion for a point set can be defined using the covariance matrix of
The following shows how to implement a location–scale family in a statistical package or programming environment where only functions for the "standard" version of a distribution are available. It is designed for R but should generalize to any language and library.