Average Absolute Deviation Calculator
Measure spread with the average absolute deviation from the mean, median or mode — a robust alternative to standard deviation.
How it works
AAD = ( Σ |xᵢ − c| ) ÷ n, where c is the mean or median
The average absolute deviation is the mean of how far each value lands from a chosen center, using absolute values rather than squares. Because it never squares the gaps, one huge outlier moves it far less than it moves the standard deviation, and deviating from the median gives the most robust spread of all. It reports dispersion in the data’s own units, which makes it easy to read.
Worked example
For 2, 4, 6, 8, 10 the mean is 6. The absolute gaps are 4, 2, 0, 2, 4, summing to 12, so the average absolute deviation is 12 ÷ 5 = 2.4. The population standard deviation of the same data is about 2.83 — larger, because squaring stretches the bigger gaps.
Frequently asked questions
How is this different from standard deviation?
Standard deviation squares each deviation, averages, and takes a square root, which weights large gaps heavily. Average absolute deviation just averages the raw distances, so it is smaller, in the same units, and far less sensitive to outliers.
Should I deviate from the mean or the median?
The absolute deviation is mathematically smallest when measured from the median, making that the most robust choice for skewed data. Deviating from the mean is the more common textbook definition and pairs naturally with other mean-based statistics.
When is average absolute deviation preferred?
It shines when you want a spread measure that resists outliers and reads in plain units — for example describing typical forecast error — without the squaring that standard deviation applies.
Related calculators
For education — check the assumptions (sample size, independence, distribution) before using these statistics in real decisions.