Absolute deviation
From Free net encyclopedia
The absolute deviation of an element of a data set is the absolute difference between that element and a given point. Typically the point from which the deviation is measured is the value of either the median or the mean of the data set.
- <math>|D| = |x_i-\hat{x}| </math>
where
- |D| is the absolute deviation,
- xi is the data element
- and <math>\hat{x}</math> is the chosen measure of central tendency of the data set.
The average absolute deviation (or simply average deviation) of a data set is the average (or expected value) of the absolute deviations and is a summary statistic of statistical dispersion or variability.
The average absolute deviation of a set {x1, x2, ..., xn} is:
- <math>\frac{1}{n}\sum_{i=1}^n |x_i-\hat{x}|</math>
The type of central tendency chosen has a significant effect on the value of the average deviation. For example, for the set {1,2,2,4,6}, the median is 2 while the mean is 3. The average absolute deviation from the median is (1+0+0+2+4)/5=1.4 while the average absolute deviation from the mean (sometimes called the mean deviation) is (2+1+1+1+3)/5=1.6.
In general, the average absolute deviation from the mean is between one and two times the average absolute deviation from the median; it is also less than or equal to the standard deviation.no:Absolutt avvik pl:Odchylenie bezwzględne sv:Genomsnittlig avvikelse