Median Absolute Deviation Calculator
A Measure of Spread That Outliers Can't Distort
Standard deviation squares every deviation from the mean, which means a single extreme value can dominate the entire result. The median absolute deviation sidesteps that problem entirely by using medians throughout — the median of the data, then the median of the absolute distances from it — making it one of the most outlier-resistant measures of spread available.
The Formula
First find the median of the data set. Then compute the absolute distance of every value from that median. The MAD is the median of those distances.
How Resistant It Really Is
Take six measurements where one is a clear outlier:
| Data set | Median | MAD | Sample Std Dev |
|---|---|---|---|
| 10, 12, 13, 12, 11, 50 | 12 | 1 | 15.71 |
The outlier at 50 inflates the standard deviation by more than fifteenfold over the typical spacing of the data, while the MAD stays at 1 — a far more honest description of how tightly the bulk of the readings actually cluster.
Where This Matters
- Outlier detection — MAD-based thresholds are commonly used to flag anomalous data points precisely because MAD itself isn't skewed by those same outliers.
- Financial data — asset returns often include rare extreme days; MAD gives a more stable baseline volatility measure than standard deviation.
- Sensor and instrument data — filtering out glitches or transient spikes without discarding the entire reading history.
- Robust statistics generally — any analysis where a handful of bad data points shouldn't be allowed to dominate the summary.
How to Use This Calculator
- Enter your numbers into the values field, separated by commas.
- Select Calculate.
- The result shows the median, each value's absolute deviation from it, and the resulting MAD.
Related Calculations
Compare this against the Standard Deviation Calculator to see how much outliers are affecting your spread measurement, or use the Median Calculator to find the central value on its own.