# Average absolute deviation

**mean absolute deviationmean deviationMADmaximum absolute deviation**

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

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### Median

**averagesample medianmedian-unbiased estimator**

In this general form, the central point can be the mean, median, mode, or the result of another measure of central tendency.

When the median is used as a location parameter in descriptive statistics, there are several choices for a measure of variability: the range, the interquartile range, the mean absolute deviation, and the median absolute deviation.

### Standard deviation

**standard deviationssample standard deviationsigma**

The mean absolute deviation from the mean is less than or equal to the standard deviation; one way of proving this relies on Jensen's inequality.

It is algebraically simpler, though in practice less robust, than the average absolute deviation.

### Deviation (statistics)

**deviationabsolute deviationdeviations**

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

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

### Statistical dispersion

**dispersionvariabilityspread**

It is a summary statistic of statistical dispersion or variability.

Average absolute deviation (or simply called average deviation)

### Central tendency

**Localitycentral locationcentral point**

In this general form, the central point can be the mean, median, mode, or the result of another measure of central tendency.

### Sample maximum and minimum

**sample maximumsample minimumMaximum**

While not strictly a measure of central tendency, the maximum absolute deviation can be found using the formula for the average absolute deviation as above with, where \max(X) is the sample maximum.

They also realize the maximum absolute deviation: one of them is the furthest point from any given point, particularly a measure of center such as the median or mean.

### Mean absolute error

Mean absolute error

The mean absolute error is a common measure of forecast error in time series analysis, sometimes used in confusion with the more standard definition of mean absolute deviation.

### Bias of an estimator

**unbiasedunbiased estimatorbias**

The mean absolute deviation of a sample is a biased estimator of the mean absolute deviation of the population.

A minimum-average absolute deviation median-unbiased estimator minimizes the risk with respect to the absolute loss function (among median-unbiased estimators), as observed by Laplace.

### Mid-range

**midsummarymidrangehalf-range**

L ∞ norm statistics: the mid-range minimizes the maximum absolute deviation

While the mean of a set of values minimizes the sum of squares of deviations and the median minimizes the average absolute deviation, the midrange minimizes the maximum deviation (defined as ): it is a solution to a variational problem.

### Least absolute deviations

**LADleast absolute deviationleast absolute deviation (LAD) regression**

Least absolute deviations

Average absolute deviation

### Median absolute deviation

**MAD**

Median absolute deviation

Average absolute deviation

### Average

**Rushing averageReceiving averagemean**

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

Average absolute deviation

### Absolute value

**modulusabsolutemagnitude**

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

### Summary statistics

**summary statisticSummarizationdata summarization**

It is a summary statistic of statistical dispersion or variability.

### Arithmetic mean

**meanaveragearithmetic**

In this general form, the central point can be the mean, median, mode, or the result of another measure of central tendency.

### Mode (statistics)

**modemodalmodes**

### Jensen's inequality

**See here**

The mean absolute deviation from the mean is less than or equal to the standard deviation; one way of proving this relies on Jensen's inequality.

### Square root

**square rootssquareradical**

Since both sides are positive, and the square root is a monotonically increasing function in the positive domain:

### Inequality (mathematics)

**inequalityinequalitiesless than**

Since both sides are positive, and the square root is a monotonically increasing function in the positive domain:

### Hölder's inequality

For a general case of this statement, see Hölder's inequality.

### Normal distribution

**normally distributednormalGaussian**

For the normal distribution, the ratio of mean absolute deviation to standard deviation is.

### Mean squared error

**mean square errormean-squared errorsquared error loss**

This method's forecast accuracy is very closely related to the mean squared error (MSE) method which is just the average squared error of the forecasts.

### Maximum likelihood estimation

**maximum likelihoodmaximum likelihood estimatormaximum likelihood estimate**

This is the maximum likelihood estimator of the scale parameter b of the Laplace distribution.

### Laplace distribution

**Laplacedouble exponentialLaplace distributed**

This is the maximum likelihood estimator of the scale parameter b of the Laplace distribution.

### Robust measures of scale

**Qn estimatorrobust estimator of dispersionrobust measure of scale**

It is a robust estimator of dispersion.