Median Absolute Deviation Calculator
Enter your dataset to calculate the median and the median absolute deviation for robust dispersion analysis.
Median
19.5000
Median Absolute Deviation
4.5000
Observation count: 6
MAD is the median of absolute deviations from the dataset median, providing strong resistance to outliers.
How to Use This Calculator
- Enter numerical observations separated by spaces or commas.
- Review the median and MAD outputs.
- Use MAD to evaluate variability when datasets contain outliers.
- Compare MAD across datasets to judge consistency robustly.
Formula
MAD = median(|xi − median(x)|)
Scaling for normal distributions (optional): MAD × 1.4826 ≈ standard deviation
The optional scaling factor aligns MAD with standard deviation for normally distributed data.
Full Description
Median absolute deviation is a robust alternative to standard deviation, ideal when data include extreme outliers or heavy tails. It emphasizes the central bulk of the distribution, making it common in quality control and anomaly detection.
Because MAD relies on medians, it is unaffected by a few extreme points, providing stability in noisy environments.
Frequently Asked Questions
Is MAD better than standard deviation?
Neither is universally better. MAD is more robust to outliers; standard deviation works well for symmetric, light-tailed distributions.
Can I apply MAD to small datasets?
Yes, but with very small samples MAD may be zero or unstable. More observations improve reliability.
Why do I see zero MAD?
If all values are identical, deviations from the median are zero, leading to MAD = 0.
Should I use the 1.4826 scaling factor?
Use the factor when you want a robust estimator comparable to standard deviation under normal assumptions.