Mean Absolute Deviation Calculator
Enter a list of numbers to calculate the mean absolute deviation (MAD) — the average distance each value sits from the data set's mean, a simpler alternative to standard deviation for measuring spread.
How the Mean Absolute Deviation formula works
The MAD formula:
MAD = Σ|xᵢ − mean| / n
Step-by-step calculation
- Calculate the mean of the data set.
- Find the absolute difference between each value and the mean.
- Average those absolute differences.
Worked example
Data set: 2, 4, 6, 8. Mean = 5. Absolute deviations: 3, 1, 1, 3. MAD = (3+1+1+3)/4 = 2.
Frequently asked questions
How is MAD different from standard deviation?
MAD averages the absolute (unsquared) differences from the mean, while standard deviation squares the differences before averaging and then takes a square root. Standard deviation weights larger deviations more heavily; MAD treats all deviations proportionally.
Which measure of spread should I use?
Standard deviation is more common in formal statistics due to its mathematical properties, but MAD is simpler to compute by hand and easier to interpret intuitively as 'the typical distance from the average.'