Median Absolute Deviation Calculator

Median Absolute Deviation (MAD) measures statistical variability by evaluating how far individual data points fall from the median of the entire set. Mathematically, the formula is expressed as MAD = median(|x_i - median(X)|), where x_i represents each individual data point and X is the complete dataset. First, the calculator finds the median of your inputs. Second, it computes the absolute distance between each data point and that median. Finally, it calculates the median of those resulting absolute distances, yielding a robust metric that resists skewing from extreme values.

Imagine you have a dataset of five test scores: 12, 15, 18, 22, and 85. First, we sort the numbers in ascending order: 12, 15, 18, 22, 85. The median of this set is the middle value, which is 18. Next, we find the absolute difference between each score and the median (18): |12 - 18| = 6, |15 - 18| = 3, |18 - 18| = 0, |22 - 18| = 4, and |85 - 18| = 67. This gives us a new set of absolute deviations: 6, 3, 0, 4, 67. Sorting these deviations yields 0, 3, 4, 6, 67. The median of this new set is the middle value, 4. Therefore, the MAD is 4, proving how effectively it ignores the extreme outlier of 85.

When analyzing skewed distributions or datasets containing extreme outliers, always prefer Median Absolute Deviation over standard deviation because traditional variance heavily penalizes large anomalies. Ensure your input values are separated cleanly and double-check for missing entries before computing. If you want to use MAD as a consistent estimator for the standard deviation of a normally distributed population, multiply your final result by the standard scale factor of approximately 1.4826.