What is Median Absolute Deviation?

Median Absolute Deviation (MAD) is a robust measure of variability that calculates the median of absolute deviations from the median. It resists the influence of outliers far better than standard deviation.

MAD = median(|x_i − median(X)|)

Why MAD is Superior for Outliers:

Robust: Extreme values barely affect MAD's value. One outlier doesn't skew results.
Interpretable: Direct measure of spread in original units (not squared like SD).
Scaled MAD: Multiply by 1.4826 to match standard deviation for normal distributions (enables fair comparison).
Minimal assumptions: Works with any distribution shape, not just normal data.
Real-world data: Income, housing prices, sensor measurements often use MAD.

MAD vs Standard Deviation: SD uses squared deviations (emphasizes extremes). MAD uses absolute deviations (treats all deviations linearly). For symmetric distributions with outliers, MAD is more representative of typical spread.

How to Calculate MAD

1

Find the median

Sort dataset and locate middle value. This is the reference point for deviations.

2

Calculate deviations

For each value, compute |value − median|. Keep all deviations as positive numbers.

3

Sort the deviations

Arrange absolute deviations from smallest to largest to find their median.

4

Find the MAD

The median of absolute deviations is your MAD value. Optionally scale by 1.4826 for SD comparison.

Example Calculation

Dataset: 1, 1, 2, 2, 4, 6, 9 Step 1: Find median Sorted: [1, 1, 2, 2, 4, 6, 9] Median (middle value) = 2 Step 2: Calculate absolute deviations from median |1 - 2| = 1 |1 - 2| = 1 |2 - 2| = 0 |2 - 2| = 0 |4 - 2| = 2 |6 - 2| = 4 |9 - 2| = 7 Step 3: Sort the deviations Sorted deviations: [0, 0, 1, 1, 2, 4, 7] Step 4: Find median of deviations MAD = median = 1 (middle value of 7 deviations) Step 5: Scale MAD (optional) Scaled MAD = 1 × 1.4826 = 1.4826 Use this for comparing to standard deviation (≈ 2.19 for this dataset)

Median Absolute Deviation Calculator

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