Mean Absolute Deviation (MAD) is the average absolute deviation from the mean. It’s more robust to outliers than standard deviation because it uses absolute values instead of squares.

Formula

Ungrouped Data:

MAD = Σ|xᵢ - x̄| / n

Grouped Data:

MAD = Σ(fᵢ|xᵢ - x̄|) / Σfᵢ

Example (Ungrouped)

Dataset: 10, 15, 20, 25, 30 Mean = 20

Absolute deviations: |10-20| = 10, |15-20| = 5, |20-20| = 0, |25-20| = 5, |30-20| = 10

MAD = (10 + 5 + 0 + 5 + 10) / 5 = 30 / 5 = 6

Interpretation: Values deviate from the mean by an average of 6 units.

Advantages vs Standard Deviation

✅ More interpretable - Same units, no squaring confusion ✅ More robust - Less affected by outliers ✅ Easier to calculate - No squaring or square root

❌ Less convenient mathematically - Not used in many statistical tests ❌ Less sensitive - May miss subtle distribution changes

When to Use MAD

  • Robust measure of spread needed
  • Outliers present in data
  • Need interpretable dispersion measure
  • Distribution not approximately normal