Average distance of each value from the mean — with worked steps
Enter your numbers to calculate the mean absolute deviation (MAD) — the average distance of the values from their mean. The mean, standard deviation and other statistics are shown alongside.
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The mean absolute deviation (MAD) measures spread by averaging how far each value lies from the mean, using absolute distances. Because it takes the absolute value of each deviation rather than squaring it, the MAD is in the same units as the data and is not inflated by extreme values the way the standard deviation can be.
Find the mean, take the absolute difference between each value and the mean, then average those distances: MAD = (Σ|xᵢ − x̄|) ÷ n. The result is always zero or positive, and it is zero only when every value is identical.
Both describe spread, but they treat outliers differently. The standard deviation squares each deviation, so values far from the mean dominate it; the MAD weighs every deviation linearly, making it more robust and often easier to explain. The standard deviation is more common in formal statistics because of its mathematical properties, while the MAD is popular in teaching and in forecasting accuracy.
Compute the mean, find the absolute difference between each value and the mean, add those differences, and divide by the number of values.
MAD averages the absolute deviations; standard deviation is based on squared deviations. MAD is less sensitive to outliers and stays in the original units.
No. It is an average of absolute (non-negative) distances, so it is always zero or positive.