Mean Absolute Deviation Calculator
Mean absolute deviation (MAD) is the average absolute distance of observations from their arithmetic mean. It describes typical distance from the centre while keeping deviations in the same unit as the observations.
How to use this calculator
- Enter at least two numeric values; the calculator finds their mean and averages each value's absolute distance from it.
- Review the worked deviation example and compare its arithmetic with the inputs you plan to use.
- Change one input at a time when exploring a different scenario, and keep units and assumptions consistent.
Mean absolute deviation
MAD about the mean = Σ|x − mean| ÷ n.
- Absolute values make both positive and negative deviations contribute a non-negative distance to the spread measure.
- The page's numerical output is calculated from the values entered; it does not independently verify whether those inputs fit the real-world situation.
Worked examples
Deviation example
For values 2, 4, and 6, the mean is 4 and absolute deviations are 2, 0, and 2.
(2 + 0 + 2) ÷ 3 = 1.3333
Mean absolute deviation is about 1.333 units.
Understanding the result
MAD about the mean remains in the original units and is less affected by large deviations than squared-deviation measures in some settings.
This is not the median absolute deviation, which measures distance from the median instead.
Important notes
Check which definition of MAD a textbook, analysis tool, or report expects.
Displayed values may be rounded for readability. Keep appropriate precision for intermediate calculations and check the unit labels before using the result.
Frequently asked questions
What does the Mean Absolute Deviation Calculator result mean?
MAD about the mean remains in the original units and is less affected by large deviations than squared-deviation measures in some settings.
What should I check before using the mean absolute deviation calculator?
Check which definition of MAD a textbook, analysis tool, or report expects.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- Z-Score — Learn what a z-score measures and how it describes a value relative to a mean and standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.