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The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it ...
Suppose there were 100 objects and the operator weighed them all, one at a time, and repeated the whole process ten times. Then the operator can calculate a sample standard deviation for each object, and look for outliers. Any object with an unusually large standard deviation probably has an outlier in its data.
The sample maximum and minimum are the least robust statistics: they are maximally sensitive to outliers.. This can either be an advantage or a drawback: if extreme values are real (not measurement errors), and of real consequence, as in applications of extreme value theory such as building dikes or financial loss, then outliers (as reflected in sample extrema) are important.
For a symmetric distribution (where the median equals the midhinge, the average of the first and third quartiles), half the IQR equals the median absolute deviation (MAD). The median is the corresponding measure of central tendency. The IQR can be used to identify outliers (see below). The IQR also may indicate the skewness of the dataset. [1]
This makes median absolute deviation less sensitive to outliers, offering a robust alternative to standard deviation. [9] Maximum absolute deviation is a straightforward measure of the maximum difference between any individual data point and the mean of the dataset. However, it is highly non-robust, as it can be disproportionately influenced by ...
Median absolute deviation (MAD) Average absolute deviation (or simply called average deviation) Distance standard deviation; These are frequently used (together with scale factors) as estimators of scale parameters, in which capacity they are called estimates of scale. Robust measures of scale are those unaffected by a small number of outliers ...
The modified Thompson Tau test is used to find one outlier at a time (largest value of δ is removed if it is an outlier). Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set.
In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950 [1]), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate data set assumed to come from a normally distributed population.