Mean Absolute Deviation (MAD) measures the average distance of data points from a central value. It's a robust alternative to standard deviation.

MAD = Σ|xᵢ − center| / n

Key Characteristics:

• Robust to outliers: Absolute deviations don't amplify extreme values like squared deviations do.
• Interpretable: Expressed in original data units (unlike variance which is in squared units).
• Two versions: MAD around mean or MAD around median (median is more robust).
• Relationship to SD: For normal data, MAD ≈ 0.8 × Standard Deviation.
• Box plot connection: IQR and MAD are both robust spread measures used in exploratory analysis.

When to use: Skewed distributions, small samples, outlier-prone data, or when you need simple interpretability.