Mean Absolute Deviation Calculator

The Mean Absolute Deviation is a statistical measure of data variability. It calculates the average of the absolute distances between each data point and the center of the dataset (mean or median). Unlike standard deviation, MAD uses absolute differences rather than squared differences, making it more intuitive and less sensitive to outliers.

The formula is MAD = Σ|xᵢ − x̄| / n, where xᵢ is each data point, x̄ is the mean (or median) of the dataset, and n is the number of values. You sum up all the absolute differences between each point and the center, then divide by the count of values.

Simply type or paste your numeric values into the dataset field, separated by commas. Choose whether you want to calculate MAD around the mean or the median, then click Calculate. The tool returns the MAD, sample size, center value, sum of absolute differences, and a full deviation table.

Mean Absolute Deviation uses the arithmetic mean as the center, which works well for symmetric, normally distributed data. Median Absolute Deviation is more robust when your data contains outliers or is skewed, since the median is not pulled by extreme values. This calculator supports both options.

Without absolute values, positive and negative deviations would cancel each other out, and the sum of all deviations from the mean is always exactly zero. Taking the absolute value ensures every deviation contributes positively to the total, giving a true measure of how spread out the data is.

Both measure data spread, but standard deviation squares the differences before averaging (then takes a square root), which amplifies the effect of outliers. MAD uses absolute differences, so it is more interpretable in the original units and less distorted by extreme values. MAD is often preferred in introductory statistics for its simplicity.

Common mistakes include forgetting to take the absolute value of each difference (so negative deviations cancel positives), dividing by n−1 instead of n (MAD always uses n, not the sample variance formula), and confusing Mean Absolute Deviation with Median Absolute Deviation. Make sure all your input values are numeric — non-numeric entries are ignored.

MAD is used in finance to measure portfolio volatility, in forecasting to evaluate prediction error (Mean Absolute Error is essentially MAD), in quality control to monitor manufacturing consistency, and in education to explain variability concepts before introducing standard deviation. Any field that needs a straightforward measure of spread can benefit from MAD.