# Deviation

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A Deviation is the difference between the data values of a quantity and its expected value or an estimation of its true value.

**See:**Absolute Deviation, Average Absolute Deviation, Mean Deviation, Standard Deviation, Statistical Dispersion.

## References

### 2016

- (Wikipedia, 2016) ⇒ http://www.wikiwand.com/en/Deviation_(statistics) Retrieved 2016-07-10
- 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 (positive or negative), 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.

- In mathematics and statistics,

**Types of deviation**

- 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**. These concepts are applicable for data at the interval and ratio levels of measurement.

**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.

- [math]\displaystyle{ D_i = |x_i-m(X)| }[/math]
- where
*D*_{i}is the absolute deviation,*x*_{i}is the data element- and
*m*(*X*) is the chosen measure of central tendency of the data set — sometimes the mean ([math]\displaystyle{ \overline{x} }[/math]), but most often the median.

**Measures of deviation**

**Mean signed deviation**- For an unbiased estimator, the average of the signed deviations across the entire set of all observations from the unobserved population parameter value averages zero over an arbitrarily large number of samples. However, by construction the average of signed deviations of values from the sample mean value is always zero, though the average signed deviation from another measure of central tendency, such as the sample median, need not be zero.
**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,**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.

### 2016

- (Eric W. Weisstein , 2016) ⇒ Weisstein, Eric W. (1999-2016)"Deviation." From MathWorld -- A Wolfram Web Resource. http://mathworld.wolfram.com/Deviation.html Retrieved 2016-07-10
- The difference of a quantity from some fixed value, usually the "correct" or "expected" one.