Mean Absolute Deviation Calculator
Paste a list of numbers to get the mean absolute deviation (MAD), plus the mean, variance and standard deviation.
How it works
MAD = Σ|x − mean| ÷ n · variance (σ²) = Σ(x − mean)² ÷ n · σ = √variance
The mean absolute deviation measures spread as the plain average distance of each value from the mean, using absolute values so positive and negative gaps don’t cancel. It is easier to interpret than the standard deviation — it is a real average distance in the original units — but it weights every deviation equally, whereas variance and standard deviation square the gaps and so react more strongly to extreme values. These figures use the population divisor n.
Worked example
For 4, 8, 6, 5, 3, 9, 7 the mean is 42 ÷ 7 = 6. The absolute deviations are 2, 2, 0, 1, 3, 3, 1, which sum to 12, so MAD = 12 ÷ 7 ≈ 1.7143. The squared deviations sum to 28, giving a variance of 4 and a standard deviation of 2.
Frequently asked questions
How is MAD different from standard deviation?
Both measure spread, but MAD averages the absolute distances while standard deviation averages the squared distances and then takes a root. Squaring makes standard deviation more sensitive to outliers, so MAD is the more robust, plain-language measure.
Why is MAD usually smaller than the standard deviation?
Squaring inflates larger deviations, pushing the standard deviation up, so for most data sets MAD comes out lower. For a normal distribution the MAD is about 0.8 times the standard deviation.
Should I divide by n or n − 1?
This calculator uses n, treating your numbers as the whole population. If they are a sample meant to estimate a larger group, some texts divide the squared deviations by n − 1 for the variance; the MAD itself is normally reported with n.
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