Calculators5 min readUpdated: 2026-09-16

Mean Absolute Deviation

Definition

Mean Absolute Deviation (MAD) is a measure of statistical dispersion representing the average distance between each data point in a dataset and the arithmetic mean.

Detailed Technical Breakdown

Calculated by averaging the absolute differences |x_i - mean|, Mean Absolute Deviation quantifies variability without squaring deviations. Because it treats all errors linearly rather than quadratically, MAD is intuitive to interpret and robust against extreme outliers that would otherwise disproportionately distort standard deviation.

Key Technical Specifications

  • Formula: MAD = (1/n) * Sum(|x_i - mean|).
  • Preserves original measurement units without square roots.
  • Outlier relationship: For normal distributions, Standard Deviation ≈ 1.253 * MAD.
  • Equivalent to Mean Absolute Error (MAE) in machine learning and forecasting.

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