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What Is Median Absolute Deviation?
The Median Absolute Deviation (MAD) is a robust measure of variability. It calculates the median of the absolute deviations from the data's median. Unlike standard deviation, MAD is highly resistant to outliers, making it ideal for datasets with extreme values.
MAD is used in robust statistics, anomaly detection, and quality control. It provides a reliable measure of spread even when data contains errors or unusual observations that would strongly influence the standard deviation.
Formula
The constant 1.4826 converts MAD to an equivalent standard deviation estimate for normally distributed data.
Advantages of MAD
| Feature | MAD | Standard Deviation |
|---|---|---|
| Robustness | Very high (50% breakdown) | Low (one outlier can dominate) |
| Computation | Uses medians | Uses means and squares |
| Outlier influence | Minimal | Significant |
| Efficiency (normal) | 37% | 100% |
Frequently Asked Questions
What does the 1.4826 constant mean?
For normally distributed data, the MAD is approximately 67.45% of the standard deviation. The constant 1.4826 = 1/0.6745 scales MAD to match the standard deviation, providing a consistent estimator for σ.
When should I use MAD instead of standard deviation?
Use MAD when your data may contain outliers, measurement errors, or comes from heavy-tailed distributions. MAD is commonly used in financial risk analysis, signal processing, and data cleaning.
What is the breakdown point of MAD?
MAD has a breakdown point of 50%, meaning up to half the data can be corrupted before the measure becomes unreliable. Standard deviation has a breakdown point of 0%, meaning a single extreme outlier can make it arbitrarily large.