Find the mean absolute deviation (MAD) of a dataset — the average distance each data point sits from the mean.
How it works
First find the mean, then average the absolute distance of every point from it: MAD = mean(|xᵢ – mean|). The dataset 2, 4, 4, 4, 5, 5, 7, 9 has a MAD of 1.5.
What this does not include
This is distinct from this site’s standard deviation calculator, whose own scope explicitly covers variance and standard deviation — squared-then-rooted distances — rather than this linear absolute-distance measure. The two summarize spread differently and aren’t interchangeable.
How to use this calculator
- Enter your data as comma-separated numbers.
A worked example
Dataset 2, 4, 4, 4, 5, 5, 7, 9: mean absolute deviation = 1.5.
Dataset 1, 2, 3, 4, 5: mean absolute deviation = 1.2.
What the variables mean
| Variable | Meaning |
|---|---|
| Data | The full dataset, comma-separated |
| MAD | Average distance of each value from the dataset’s mean |
Edge cases worth knowing
MAD uses absolute distances, so it’s always non-negative — values above and below the mean both contribute positively, unlike a plain average of signed deviations, which always cancels out to zero.
An empty dataset has no mean to measure distance from, so the calculator declines to show a result.
Why use MAD instead of standard deviation?
MAD is less sensitive to extreme outliers than standard deviation, since it doesn’t square the distances — a few very large deviations pull standard deviation up more sharply than they pull MAD.
Can MAD ever be zero?
Yes — if every data point is identical, there’s no spread at all, and MAD comes out to exactly zero.
Is MAD always smaller than standard deviation?
Generally, yes, for the same dataset — since squaring distances before averaging (as standard deviation does) tends to weight larger deviations more heavily than simple absolute distances do.
