average absolute deviation

The authors found an average absolute deviation of 10.6% against their database of experimental data.

Alternatives such as average absolute deviation and semivariance have been advanced for measuring financial risk.

It is algebraically simpler though practically less robust than the average absolute deviation.

Average absolute deviation (or simply called average deviation)

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

Similarly, the average absolute deviation needs to be multiplied by approximately 1.2533 to be a consistent estimator for standard deviation.

The coefficient of dispersion (CD) is defined as the ratio of the average absolute deviation from the median to the median of the data.

In fact, the average absolute deviation from the median is always less than or equal to the average absolute deviation from any other fixed number.

Note that the median in this sense is not in general unique, and in fact any point between the two central points of a discrete distribution minimizes average absolute deviation.

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 is the sample maximum.

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.

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.

The mean absolute deviation (MAD), also referred to as the mean deviation (or sometimes average absolute deviation, though see above for a distinction), is the mean of the absolute deviations of a set of data about the data's mean.