How to use this mean absolute deviation calculator
Paste your numbers above and press Calculate. You get the MAD together with every value's absolute deviation, so the "average distance" idea is visible, not just named.
The most intuitive spread of all
Ask a class how spread out numbers are and someone will eventually say: "on average, how far is each number from the average?" That is the mean absolute deviation, arguably the most natural spread measure ever defined. Take the mean, measure each value's distance from it (ignoring direction), and average those distances. No squares, no roots.
Five values: 4, 8, 6, 10, 7. The mean is 7. Distances from 7: 3, 1, 1, 3, 0, and averaging gives MAD = 1.6. Interpretation needs no training: values in this dataset sit, on average, 1.6 units from their mean.
So why does standard deviation rule instead?
History and algebra. Squared deviations are smooth and differentiable, play nicely with the normal distribution, and add up across independent variables. Absolute values do none of these favours. The MAD survives where interpretation matters more than algebra: outlier-resistant statistics, forecasting error (as MAE), and classrooms, where it builds the intuition that the standard deviation later formalises. For roughly normal data, SD ≈ 1.25 × MAD, a handy conversion.
Frequently asked questions
What is the difference between MAD and standard deviation?
MAD averages the absolute distances from the mean; standard deviation averages squared distances and then takes the square root. Squaring penalises large deviations more, so SD is the larger, more outlier-sensitive measure.
Why is MAD not used more often?
Absolute values are mathematically awkward: not differentiable at zero and hard to combine across variables. Squared deviations support the algebra statistics is built on.
Does MAD here mean mean or median absolute deviation?
This calculator gives the mean absolute deviation (distances from the mean). A separate calculator covers the median absolute deviation, an outlier-resistant statistic with a different centre.