Mean Absolute Deviation Calculator
Calculate the mean absolute deviation (MAD) of a data set. MAD measures the average distance between each data point and the mean.
Enter a data set to calculate MAD.
MAD Formula
MAD = (1/n) × Σ|xᵢ − x̄|
The mean absolute deviation is the average of the absolute differences between each value and the mean. It provides a simple measure of variability.
How to Calculate MAD
- Find the mean (x̄) of the data set.
- For each value, calculate |xᵢ − x̄| (absolute deviation).
- Find the mean of all absolute deviations.
Example: Data: 2, 4, 6, 8, 10
Mean = 6
Absolute deviations: |2−6|=4, |4−6|=2, |6−6|=0, |8−6|=2, |10−6|=4
MAD = (4+2+0+2+4)/5 = 2.4
Mean = 6
Absolute deviations: |2−6|=4, |4−6|=2, |6−6|=0, |8−6|=2, |10−6|=4
MAD = (4+2+0+2+4)/5 = 2.4
MAD vs Standard Deviation
- MAD uses absolute values — easier to interpret and more robust to outliers.
- Standard deviation uses squared differences — more mathematically convenient and commonly used in statistics.
- For normally distributed data: SD ≈ 1.2533 × MAD.
FAQ
When should I use MAD instead of standard deviation?
Use MAD when your data has outliers, when you want a measure that's easy to explain, or when working with non-normal distributions.
Can MAD be zero?
Yes, MAD equals zero only when all values in the data set are identical (no spread at all).
Related Calculators
Last updated: 2026-08-08