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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Mean absolute deviation
Based on 5 values, the average absolute distance from the mean is 3.6.
5
Mean
4.56
Standard deviation
12
Range
0.79
MAD / SD ratio
These summary rows show the centre and scale values that feed the mean absolute deviation.
| Count | 5 |
|---|---|
| Sum | 25 |
| Mean | 5 |
| Median | 3 |
| Minimum | 2 |
| Maximum | 14 |
| Range | 12 |
| Sum of absolute deviations | 18 |
MAD averages these absolute distances from the mean rather than squaring them.
| # | Value | Deviation from mean | Absolute deviation |
|---|---|---|---|
| 1 | 2 | -3 | 3 |
| 2 | 2 | -3 | 3 |
| 3 | 3 | -2 | 2 |
| 4 | 4 | -1 | 1 |
| 5 | 14 | 9 | 9 |
This comparison helps you see how a linear spread measure differs from a squared-deviation spread measure.
| Measure | Value | Why it matters |
|---|---|---|
| Mean absolute deviation | 3.6 | Average absolute distance from the mean in the original units. |
| Standard deviation | 4.56 | Spread measure that squares deviations before averaging. |
| MAD to SD ratio | 0.79 | Helps show whether squared-deviation spread is much larger than absolute-deviation spread. |
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.
The MAD is easiest to read as a typical distance from the mean in the original units of the data. If a class test dataset has a mean score of 72 and a MAD of 4, the practical reading is that scores sit about 4 points away from the mean on average. That is often more intuitive than variance because there are no squared units to mentally undo.
It is still important to compare the MAD with the shape of the dataset. A moderate MAD can come from many small deviations spread across the whole list, or from one or two very large deviations plus many values near the mean. That is why this page pairs the headline result with the absolute-deviation steps and a standard-deviation comparison instead of showing only one number.
MAD is often a better descriptive choice when you want an average-distance explanation rather than a formula that magnifies extreme values. Teachers use it when introducing spread in an intuitive way, analysts use it when they want a robust descriptive check before moving into heavier inferential methods, and quality-control users sometimes prefer it when one unusual reading should not dominate the whole story.
That does not make MAD a replacement for standard deviation everywhere. Standard deviation is still more common in formal statistical modelling because it connects directly to variance, normal-theory formulas, and many hypothesis tests. A strong workflow is to use MAD for immediate interpretability, then compare it with the standard deviation when you want to see whether outliers are stretching the spread disproportionately.
Take the dataset [10, 10, 11, 12, 30]. The mean is 14.6. The absolute deviations from the mean are 4.6, 4.6, 3.6, 2.6, and 15.4, which sum to 30.8. Dividing by 5 gives a MAD of 6.16.
Now compare that with the standard deviation for the same dataset. Because standard deviation squares the deviations first, the high value 30 has a much larger effect on the final spread measure than it does in MAD. That difference is the practical reason to compare the two measures side by side: if standard deviation rises much faster than MAD, the dataset may be being pulled by one or two extreme observations rather than broad overall variability.
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.
No. This calculator uses the mean absolute deviation from the arithmetic mean. Median absolute deviation is a different statistic that uses the median as the centre and is often more robust to outliers.
MAD is often easier to interpret and can be more robust when a dataset contains outliers or heavy tails. Standard deviation is more common in many statistical formulas, but MAD is a good descriptive-spread measure when you want a simpler average-distance interpretation.
A high MAD means values sit farther from the mean on average. It does not automatically mean the data are wrong or that there are outliers, only that the dataset is less tightly clustered around its centre.
Comparing the two helps you see whether the spread is broadly shared across the whole dataset or whether a few larger deviations are inflating the squared-deviation measure much faster than the absolute-deviation measure.
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