Calculate mean absolute deviation (MAD) for any dataset. Find data spread around the mean or median with step-by-step deviation tables and charts.
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Calculate mean absolute deviation (MAD) to measure how spread out your data is from the central point. Choose between mean or median as the center, view detailed deviation tables, and understand your data distribution with step-by-step calculations.
Mean Absolute Deviation (MAD) is a measure of variability that describes the average distance between each data point and the mean (or median) of the dataset. Unlike variance and standard deviation which square the differences, MAD uses absolute values, making it more intuitive and less sensitive to outliers. MAD is often preferred in education and practical applications because it's easier to interpret - it tells you the average 'distance' from the center in the same units as your data.
MAD Formula
Monitor manufacturing consistency by measuring how much product measurements deviate from specifications.
Assess investment risk and portfolio volatility in terms of average deviation from expected returns.
Evaluate forecast accuracy by calculating average deviation between predictions and actual temperatures.
Measure data consistency in experiments and surveys with a robust, outlier-resistant statistic.
More intuitive than variance - results are in original units
Less affected by extreme outliers than standard deviation
Easy to calculate and understand
Useful for comparing variability between datasets
Preferred measure in forecast accuracy and error analysis
Both measure spread, but standard deviation squares the differences (giving more weight to outliers) while MAD uses absolute values. For normal distributions, MAD ≈ 0.8 × standard deviation. MAD is more intuitive as it's in original units and less sensitive to extreme values.
Use the mean for symmetric data or when comparing with standard deviation. Use the median when your data has outliers or is skewed - MAD around the median is mathematically the smallest possible average absolute deviation.
This is a mathematical property proven using Jensen's inequality. Since squaring emphasizes larger deviations more than taking absolute values, variance (and thus standard deviation) is always at least as large as MAD squared.
MAD is preferred when you need an intuitive measure in original units, when dealing with outliers, in forecast accuracy measurement (like MAE), and in educational contexts where the concept needs to be easily understood.