Deviation

In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean. The sign of the deviation reports the direction of that difference (the deviation is positive when the observed value exceeds the reference value). The magnitude of the value indicates the size of the difference.

Types
A deviation that is a difference between an observed value and the true value of a quantity of interest (such as a population mean) is an error and a deviation that is the difference between the observed value and an estimate of the true value (such an estimate may be a sample mean) is a residual.

Unsigned or absolute deviation
In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the deviation is reckoned from the central value, being construed as some type of average, most often the median or sometimes the mean of the data set.


 * $$D_i = |x_i-m(X)| $$

where


 * $$D_i$$Di is the absolute deviation,
 * xi is the data element
 * and m(X) is the chosen measure of central tendency of the data set—sometimes the mean ($$\overline{x}$$), but most often the median.

Measures
Statistics of the distribution of deviations are used as measures of statistical dispersion, such as the frquently used standard deviation. It uses squared deviations, and has desirable properties.