Deviation (statistics)

In mathematics and statistics, deviation is a measure of difference for interval and ratio variables between the observed value and the mean. The sign of deviation (positive or negative), reports the direction of that difference (it is larger when the sign is positive, and smaller if it is negative). The magnitude of the value indicates the size of the difference.

Deviations are known as errors or residuals: deviations from the population mean are errors, while deviations from the sample mean are residuals.

The sum of the deviations across the entire set of all observations from the mean is always zero, and the average deviation is zero.

Measures of deviation

Dispersion

Statistics of the distribution of deviations are used as measures of statistical dispersion.

Standard deviation is the frequently used measure of dispersion: it uses squared deviations, and has desirable properties, but is not robust.

Average absolute deviation, sometimes called the "average deviation" is calculated using the absolute value of deviation – it is the sum of absolute values of the deviations divided by the number of observations.

Median absolute deviation is a robust statistic which uses the median, not the mean, of absolute deviations.

Maximum absolute deviation is a highly non-robust measure, which uses the maximum absolute deviation.

Dimensional analysis

For more on Studentizing, see Studentization, Studentized residual, and Studentized range.

Deviations have units of the measurement scale (for instance, meters if measuring lengths); one can nondimensionalize them by dividing by a measure of scale (statistical dispersion), most often either the population standard deviation, in standardizing, or the sample standard deviation, in studentizing.

One can also scale by location, not dispersion: the formula for a percent deviation is the accepted value minus observed value divided by the observed value multiplied by 100.

See also

• Errors and residuals in statistics
• Standard score
• Studentized residual
• Absolute deviation
• Standard deviation
• Squared deviations
• Variance

This statistics-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Statistical terminology Statistics stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем решить контрольную работу Skerne Red Barn Observatory Look at other dictionaries: Deviation — may refer to: Deviation (statistics), the difference between the value of an observation and the mean of the population in mathematics and statistics Standard deviation, which is based on the square of the difference Absolute deviation, where the …   Wikipedia deviation — n. 1 a deviating, digressing. b an instance of this. 2 Polit. a departure from accepted (esp. Communist) party doctrine. 3 Statistics the amount by which a single measurement differs from the mean. 4 Naut. the deflection of a ship s compass… …   Useful english dictionary Statistics — is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. Also with prediction and forecasting based on data. It is applicable to a wide variety of academic disciplines, from the… …   Wikipedia deviation — de vi*a tion, n. [LL. deviatio: cf. F. d[ e]viation.] 1. The act of deviating; a wandering from the way; variation from the common way, from an established rule, etc.; departure, as from the right course or the path of duty. [1913 Webster] 2. The …   The Collaborative International Dictionary of English Deviation of a falling body — deviation de vi*a tion, n. [LL. deviatio: cf. F. d[ e]viation.] 1. The act of deviating; a wandering from the way; variation from the common way, from an established rule, etc.; departure, as from the right course or the path of duty. [1913… …   The Collaborative International Dictionary of English Deviation of the compass — deviation de vi*a tion, n. [LL. deviatio: cf. F. d[ e]viation.] 1. The act of deviating; a wandering from the way; variation from the common way, from an established rule, etc.; departure, as from the right course or the path of duty. [1913… …   The Collaborative International Dictionary of English Deviation of the line of the vertical — deviation de vi*a tion, n. [LL. deviatio: cf. F. d[ e]viation.] 1. The act of deviating; a wandering from the way; variation from the common way, from an established rule, etc.; departure, as from the right course or the path of duty. [1913… …   The Collaborative International Dictionary of English deviation — [dē΄vē ā′shən] n. [ME deviacion < LL deviatio] the act or an instance of deviating; specif., a) sharp divergence from normal behavior b) divergence from the official ideology or policies of a political party, esp. a Communist party c) the… …   English World dictionary Deviation analysis — may mean; in statistics; measurement of the absolute difference between any one number in a set and the mean of the set. in social psychology; monitoring of the behavior of people or objects within systems to measure compliance with expected or… …   Wikipedia deviation — ► NOUN 1) the action or an act of deviating. 2) Statistics the amount by which a single measurement differs from a fixed value …   English terms dictionary 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”