Median Absolute Deviation Calculator
The median absolute deviation (MAD) measures robust spread by taking the median of each observation’s absolute distance from the data median.
How to use this calculator
- Enter at least two finite data values separated by commas, semicolons or spaces.
- Check the units and definitions before comparing results with another source.
- Change one input at a time when comparing scenarios, and keep the reporting period and assumptions consistent.
Formula used by the median absolute deviation calculator
MAD = median(|xᵢ − median(x)|)
- MAD = median(|xᵢ − median(x)|)
- Different disciplines sometimes apply a normal-consistency scaling factor to MAD. This calculator reports the raw MAD and clearly labels it.
- Inputs are checked for required values and valid ranges; displayed results are rounded for readability.
Worked examples
Worked example
Values 2, 3, 3, 4, 10 have median 3.
Absolute deviations are 1, 0, 0, 1, 7; their median is 1.
Absolute deviations are 1, 0, 0, 1, 7; their median is 1.
Understanding the result
The median absolute deviation (MAD) measures robust spread by taking the median of each observation’s absolute distance from the data median.
Different disciplines sometimes apply a normal-consistency scaling factor to MAD. This calculator reports the raw MAD and clearly labels it.
Important notes
Different disciplines sometimes apply a normal-consistency scaling factor to MAD. This calculator reports the raw MAD and clearly labels it.
The result applies to the numbers and assumptions entered here; verify specifications for safety-critical or regulated uses.
Frequently asked questions
Why use median absolute deviation?
It is less influenced by extreme values than standard deviation in many datasets.
Is raw MAD the same as scaled MAD?
No. Some statistical methods multiply raw MAD by a constant to make it comparable to standard deviation under a normal-distribution assumption.
How do I use this calculator?
Enter at least two finite data values separated by commas, semicolons or spaces.
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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.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample 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.