Table of Contents
What Is MAD?
Mean Absolute Deviation (MAD) is a measure of variability that calculates the average absolute distance between each data point and the mean. Unlike standard deviation, MAD does not square the deviations, making it less sensitive to extreme values.
MAD provides an intuitive measure of spread: it tells you, on average, how far each data point is from the center. It is widely used in forecasting, quality control, and robust statistics where resistance to outliers is important.
Formula
Steps: 1) Find the mean. 2) Calculate the absolute deviation of each value from the mean. 3) Average the absolute deviations.
MAD vs Standard Deviation
| Feature | MAD | Standard Deviation |
|---|---|---|
| Sensitivity to outliers | Low | High |
| Mathematical properties | Limited | Rich |
| Intuitive meaning | Average distance | RMS distance |
| Normal data relation | MAD ≈ 0.7979σ | Reference measure |
Frequently Asked Questions
Is MAD always smaller than standard deviation?
For most datasets, yes. For normally distributed data, MAD is approximately 79.79% of the standard deviation. The standard deviation squares deviations, giving more weight to large deviations.
When should I use MAD instead of standard deviation?
Use MAD when your data has outliers or is not normally distributed, when you want a robust measure of spread, or when you need an easily interpretable measure of average variation.
What is the difference between MAD and median absolute deviation?
MAD (mean absolute deviation) uses the mean as the center and averages the absolute deviations. Median absolute deviation uses the median as center and takes the median of absolute deviations. The median version is even more robust to outliers.