# Deviation (statistics)

**deviationabsolute deviationdeviationsabsolute lossmaximum deviationdeviatedeviatesmagnitude of the observationsstatistical 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.wikipedia

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### Median

**averagesample medianmedian-unbiased estimator**

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.

The second inequality comes from the fact that a median minimizes the absolute deviation function

### Average absolute deviation

**mean absolute deviationmean deviationMAD**

Average absolute deviation, is the sum of absolute values of the deviations divided by the number of observations.

The average absolute deviation (or mean absolute deviation) of a data set is the average of the absolute deviations from a central point.

### Median absolute deviation

**MAD**

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

For a univariate data set X 1, X 2, ..., X n, the MAD is defined as the median of the absolute deviations from the data's median :

### Central tendency

**Localitycentral locationcentral 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.

### Absolute difference

**ordinary distance metric**

In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point.

* Absolute deviation

### Anomaly (natural sciences)

**anomaly time series**

Anomaly (natural sciences)

In the natural sciences, especially in atmospheric and Earth sciences involving applied statistics, an anomaly is the deviation in a quantity from its expected value, e.g., the difference between a measurement and a mean or a model prediction.

### Variance

**sample variancepopulation variancevariability**

Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

### Standard deviation

**standard deviationssample standard deviationsigma**

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

Deviation (statistics)

### Squared deviations from the mean

**squared deviationssum of squared deviationssum of squared differences**

Squared deviations

Absolute deviation

### Random variate

**variatedeviateobservations**

Deviate (statistics)

*Deviation (statistics)

### Mathematics

**mathematicalmathmathematician**

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.

### Statistics

**statisticalstatistical analysisstatistician**

In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point. 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.

### Mean

**mean valuepopulation meanaverage**

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. 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.

### Level of measurement

**quantitativescaleinterval scale**

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.

### Data set

**datasetdatasetsdata**

In statistics, the absolute deviation of an element of a data set is the absolute difference between that element and a given point.

### Average

**Rushing averageReceiving averagemean**

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.

### Bias of an estimator

**unbiasedunbiased estimatorbias**

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.

### Statistical dispersion

**dispersionvariabilityspread**

Statistics of the distribution of deviations are used as measures of statistical dispersion. One way is 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 (e.g., Studentized residual).

### Square (algebra)

**squaresquaredsquares**

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

### Robust statistics

**robustbreakdown pointrobustness**

Median absolute deviation is a robust statistic which uses the median, not the mean, of absolute deviations. Standard deviation is the frequently used measure of dispersion: it uses squared deviations, and has desirable properties, but is not robust.

### Nondimensionalization

**characteristic unitnondimensionalizecharacteristic units**

One can nondimensionalize in two ways.

### Standard score

**normalizednormalisednormalized score**

One way is 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 (e.g., Studentized residual).

### Studentization

**studentizingStudentized**

One way is 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 (e.g., Studentized residual).

### Studentized residual

**studentized residualsexternallystudentization of residuals**

One way is 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 (e.g., Studentized residual).

### Formula

**mathematical formulaformulaeformulas**

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