Calculate the mean absolute deviation (MAD) as a robust measure of spread — the average distance of each value from the mean.
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3.6
Mean abs. deviation
5
Mean
5
Count
| Mean absolute deviation | 3.6 |
| Mean | 5 |
| Count | 5 |
| Minimum | 2 |
| Maximum | 14 |
Also in Statistics
Descriptive Statistics
The mean absolute deviation (MAD) is the average distance of each value from the mean. It is a straightforward, intuitive measure of variability that is less sensitive to outliers than the standard deviation, because it uses absolute differences rather than squared differences.
MAD = (1/n) × Σ|xᵢ − x̄|. Calculate the mean of the dataset. Then for each value, compute the absolute difference from the mean. Sum those absolute differences and divide by n.
Example: for [2, 2, 3, 4, 14], the mean is 5. Absolute deviations: |2−5|=3, |2−5|=3, |3−5|=2, |4−5|=1, |14−5|=9. Sum = 18. MAD = 18/5 = 3.6.
The standard deviation squares deviations before averaging, giving extreme values disproportionate weight. The MAD uses absolute values, treating all deviations linearly. For a normal distribution, SD ≈ 1.25 × MAD. For distributions with heavy tails or outliers, the SD is inflated relative to the MAD.
The MAD is easier to interpret directly: "on average, values differ from the mean by 3.6 units." The standard deviation cannot be interpreted quite as directly because of the squaring.
There is a related but different measure called the median absolute deviation (also abbreviated MAD). That statistic measures the median of the absolute deviations from the median — it is even more robust to outliers. This calculator computes the mean absolute deviation (average of absolute deviations from the mean), not the median absolute deviation.
Frequently asked questions
MAD is more interpretable (it's in the same units as the data, with a direct "average distance from mean" interpretation), and it is less sensitive to outliers. Standard deviation is preferred when the data is approximately normal and for use in inferential statistics (hypothesis tests, confidence intervals) because it has nicer mathematical properties.
This calculator's MAD uses the mean, not the median. There is a separate statistic called the "median absolute deviation" (also called MAD in some contexts) which uses the median as the centre. Median absolute deviation = median(|xᵢ − median(x)|). This is even more robust to outliers and is used in robust statistics.
Yes — if all values are identical, all absolute deviations are zero and MAD = 0. A MAD of zero means the dataset has no variation; every value equals the mean.
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