Mean Absolute Deviation Calculator
The average distance from the mean, without squaring — a spread measure in the same units as the data and easier to explain than a standard deviation.
MAD = Σ|xᵢ − x̄| ÷ n.
How the mean absolute deviation calculator works
MAD = Σ|xᵢ − x̄| ÷ n. Squaring is what makes the standard deviation mathematically convenient, but it also makes it larger than the typical distance and harder to interpret. The mean absolute deviation is literally the average gap.
For normally distributed data MAD ≈ 0.7979 σ, so the standard deviation is about 25% larger than the average deviation it is often taken to be.
Formula: MAD = Σ|xᵢ − x̄| / n
Worked examples
| Inputs | Mean absolute deviation | Note |
|---|---|---|
| 2, 4, 6, 8, 10 | 2.4 | MAD = 2.4 |
| Identical values | 0 | MAD = 0 |
| With one far point | 36.75 | MAD is far below the SD |
FAQFrequently asked questions
What is the mean absolute deviation?
The average distance of the values from their mean, using absolute values instead of squares.
How is it different from the standard deviation?
The SD squares the deviations first, which weights far points more heavily and makes the result larger. For normal data the SD is about 25% bigger.
Which should I use?
The MAD if you want an honest "typical distance" that a non-specialist will understand; the SD if you need the mathematics that follows from it — confidence intervals, regression, most of statistics.
Why does statistics prefer squaring?
Because squared deviations have clean algebra: they decompose, add across independent sources, and lead to closed-form estimators. Absolute values do none of that.
Is deviation from the median different?
Yes, and it is always smaller or equal — the median is the point that minimises total absolute distance, just as the mean minimises squared distance.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.