For this outlier detection method, the median of the residuals is calculated, along with the 25th percentile and the 75th percentile. The difference between the 25th and 75th percentile is the interquartile deviation (IQD). Then, the difference is calculated between each historical value and the residual median. If the historical value is a certain number of MAD away from the median of the residuals, that value is classified as an outlier. The default threshold is 2.22, which is equivalent to 3 standard deviations or MADs.
This method is somewhat susceptible to influence from extreme outliers, but less so than the mean and standard deviation method. Box plots are based on this approach. The median and interquartile deviation method can be used for both symmetric and asymmetric data.