Mean Absolute Deviation Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
The mean absolute deviation measures the average dispersion of a dataset around its mean, by calculating the average of the absolute deviations from that mean. For the values 1, 2, 3, 4, 5, the mean is 3 and the mean absolute deviation is 1.2.
Explanation
The mean absolute deviation (MAD) is, together with variance and standard deviation, one of the most common measures of a dataset's dispersion. Its essential difference from the standard deviation lies in how it treats the individual deviations from the mean: the standard deviation squares them before averaging, then takes the square root of the result, while the mean absolute deviation simply takes their absolute value before averaging directly, with no squaring or square root. This difference has an important practical consequence: the mean absolute deviation penalizes extreme values (outliers) much less than the standard deviation, whose squaring mechanically amplifies the effect of large deviations. This is why the mean absolute deviation is sometimes preferred as a dispersion measure more robust to outliers, even though it remains less used than the standard deviation in practice — notably because it lends itself less well to certain mathematical developments used in inferential statistics, such as those relying on the confidence interval or the z-score. Like quartiles and the interquartile range, another dispersion measure robust to extreme values, these different measures answer the same question — how spread out is the data? — with different sensitivities to special cases.
Example: the values 1, 2, 3, 4, 5
Inputs
Values: 1, 2, 3, 4, 5.
Calculation
Mean = (1+2+3+4+5) ÷ 5 = 15 ÷ 5 = 3. Absolute deviations from the mean: |1−3|=2, |2−3|=1, |3−3|=0, |4−3|=1, |5−3|=2. Sum = 6. Mean absolute deviation = 6 ÷ 5 = 1.2.
Result
The mean absolute deviation of this sample is 1.2.
Frequently asked questions
What is the difference between the mean absolute deviation and the standard deviation?
The standard deviation squares each deviation from the mean before averaging, then takes the square root of the result, which mechanically amplifies the effect of extreme values. The mean absolute deviation just takes the absolute value of each deviation, with no squaring: it therefore stays more moderate with data containing a few values far from the mean.
Can the mean absolute deviation be negative?
No, never: it is an average of absolute values, which are by definition all positive or zero. The mean absolute deviation can only be zero in one case, where all the sample values are exactly identical to the mean, and therefore identical to each other.
Should you divide by n or by (n−1) to calculate the mean absolute deviation?
Unlike sample variance and standard deviation (which use a division by n−1, Bessel's correction, to correct a statistical bias), the mean absolute deviation is conventionally calculated by dividing by n, with no universally accepted equivalent correction in the statistical literature — this is the convention used by this calculator.