The median absolute deviation (MAD) is a robust measure of statistical dispersion. It quantifies the variability of a dataset by calculating the median of the absolute deviations from the data’s median. For example, if a dataset consists of the numbers 2, 4, 6, 8, and 10, the median is 6. The absolute deviations from the median are 4, 2, 0, 2, and 4. The median of these absolute deviations is 2, which is the MAD of the original dataset.
Utilizing the MAD offers several advantages over other measures of spread, such as the standard deviation, particularly when dealing with datasets containing outliers. The MAD is less sensitive to extreme values, making it a more reliable indicator of typical variability in such cases. Historically, the MAD has been employed in fields like finance and environmental science to analyze data where anomalies are common and can skew traditional statistical measures.