Median Absolute Deviation Calculator
Find the median absolute deviation (MAD), a robust spread measure.
MAD measures spread using medians, making it highly resistant to outliers.
How the Math Works
The Median Absolute Deviation (MAD) measures how spread out data points are from the center of a dataset. To calculate it, first find the median of your data. Then subtract the median from each data point and take the absolute value of each difference. Finally, find the median of these absolute deviations - that's your MAD value. Unlike standard deviation, MAD uses medians instead of means, making it resistant to extreme outliers.
Practical Applications
Use MAD when analyzing data with outliers or skewed distributions, such as financial returns, sensor readings, or biological measurements. It's particularly valuable in quality control to identify unusual variations in manufacturing processes, or in finance to detect anomalous market movements. Researchers use MAD in robust statistical methods like R's robustbase package or Python's statsmodels when traditional methods fail due to extreme values contaminating the data.
Day-to-Day Use
MAD helps you understand what's truly unusual versus what's just extreme. If your daily commute times have a MAD of 5 minutes, you'll quickly spot when a 20-minute delay is genuinely abnormal. It's useful for tracking personal metrics like sleep duration, exercise consistency, or spending patterns - telling you whether fluctuations are normal variation or worth investigating further.
Worked example
2, 4, 6, 8, 50 → MAD 2.
FAQ
MAD vs standard deviation?
MAD is robust; a single outlier can inflate the standard deviation hugely.