Average Absolute Deviation Calculator

The average absolute deviation (AAD) measures how spread out a dataset is by finding the average distance of each data point from the mean. The formula: compute the mean, find how far each value is from that mean (ignoring sign), then average those distances.

Formally: AAD = (1/n) * sum of |xi - mean|.

The absolute value is what makes this work. Without it, the deviations would cancel out to exactly zero, since positive and negative deviations always balance. By taking the absolute value, you treat “5 below the mean” the same as “5 above the mean.”

AAD is often compared to standard deviation. Both measure spread, but standard deviation squares the deviations before averaging, which weights large deviations more heavily. AAD weights all deviations equally. In practice, standard deviation is used more often because it has nicer mathematical properties (it is differentiable), but AAD is more intuitive and more robust to extreme values.

For a dataset like [2, 4, 4, 4, 5, 5, 7, 9], the mean is 5. The deviations are |2-5|, |4-5|, |4-5|, |4-5|, |5-5|, |5-5|, |7-5|, |9-5| = 3, 1, 1, 1, 0, 0, 2, 4. The sum is 12. Divide by 8 and you get AAD = 1.5. Standard deviation for the same data is about 2.0.

The median absolute deviation (MAD) is a related measure that uses the median instead of the mean as the center. MAD is even more robust against outliers, but AAD is the more commonly taught version.

AAD comes up in forecasting accuracy as the mean absolute error (MAE), where you measure how far predictions are from actuals. Same formula, different context. If your model predicts [10, 20, 30] and the actual values are [12, 18, 27], the MAE is (2+2+3)/3 = 2.33.