Median Absolute Deviation Calculator

Median absolute deviation, commonly abbreviated MAD, measures the typical distance of observations from their median. It is a robust measure of statistical dispersion, meaning that a small number of exceptionally high or low values have limited influence on the answer. This property makes MAD valuable for skewed distributions, noisy measurements, and data sets where outliers are possible or meaningful. To calculate MAD, first sort the observations and find their median. Next, compute the absolute distance from every observation to that median. Sort those distances and find their median. The resulting number is the median absolute deviation. For the values 1, 2, 3, 5, and 100, the center is 3. Their absolute distances are 2, 1, 0, 2, and 97. The median distance is 2, so the MAD is 2 even though one observation is extremely far away. This stability contrasts with measures centered on the arithmetic mean. An outlier affects the mean itself and can then enlarge many distances measured from that shifted center. Variance and standard deviation also square deviations, which gives extreme observations additional weight. Median absolute deviation depends on ranks and the middle distance, so fewer than half of the observations can change dramatically without forcing the statistic to change dramatically. Robustness is useful in many settings. A network monitoring system can summarize normal response-time variability without allowing a few outages to dominate the baseline. A laboratory can describe repeated measurements while retaining unusual readings for investigation. Financial analysts can assess typical changes in data that occasionally exhibit large jumps. MAD can also support outlier detection by comparing each observation's distance from the median with a multiple of the statistic. Some statistical software reports a scaled MAD, usually multiplying the raw result by approximately 1.4826. Under a normal distribution, that scaled value estimates the population standard deviation. This calculator reports the unscaled, raw median absolute deviation so the displayed result follows the direct definition: median(|xi − median(x)|). If a method requires the consistency-scaled version, multiply this result by the factor specified by that method. Do not confuse median absolute deviation with mean absolute deviation. They share the abbreviation MAD, but mean absolute deviation averages distances from the arithmetic mean, whereas this statistic takes the median of distances from the median. Enter integers, decimals, or negative values separated by commas or spaces. The result panel includes the center and sorted absolute deviations, making the robust calculation easy to inspect and verify.