Quick answer
Mean absolute deviation MAD = Σ|x − x̄| ÷ n. A data set with a mean of 5 and absolute deviations that sum to 12 over 8 values has a MAD of 1.5.
Enter the data. The calculator returns the MAD and the mean.
Related tools: Mean Calculator: Mean of a data set. Standard Deviation Calculator: Sample or population standard deviation with variance and mean. Geometric Mean Calculator: Geometric mean of a data set.
How to use the Mean Absolute Deviation Calculator
- Type data set, for example 4, 8, 15, 16, 23, 42.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Data set | Text, such as 4, 8, 15, 16, 23, 42 | — |
Formula and method
Formula
MAD = Σ|x − x̄| ÷ n
IEEE-754 double precision; shown to at most 6 decimal places.
Mean of absolute deviations about the arithmetic mean.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Data set = 2, 4, 4, 4, 5, 5, 7, 9.
| Result | Value |
|---|---|
| Mean absolute deviation | 1.5 |
| Mean | 5 |
Example 2
Inputs: Data set = 1, 3.
| Result | Value |
|---|---|
| Mean absolute deviation | 1 |
| Mean | 2 |
The first line is the headline result (mean absolute deviation). Below it the mean Absolute Deviation Calculator lists mean, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Compared with standard deviation
MAD is the average distance from the mean, easier to interpret than the standard deviation, which squares the deviations and weights outliers more. For the same data the standard deviation is 2, larger than the MAD of 1.5.
Details
Constant data gives 0. For normal data, SD ≈ 1.25 × MAD. Some texts use the median instead of the mean (median absolute deviation), a different, more robust measure.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Data set: left empty shows "Enter data set." beside that field and no result.
Choosing between the Mean Absolute Deviation Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Mean Calculator](/statistics/mean/) | data set | Mean |
| [Standard Deviation Calculator](/statistics/standard-deviation-calculator/) | data set and data type | Population standard deviation (σ) |
| [Geometric Mean Calculator](/statistics/geometric-mean-calculator/) | data set | Geometric mean |
| [Relative Standard Deviation Calculator](/statistics/relative-standard-deviation-calculator/) | data set and data type | Relative standard deviation |
| [Mean Median Mode Calculator](/statistics/mean-median-mode-calculator/) | data set | Mean |
Background: descriptive statistics
Population statistics divide by n and sample statistics divide by n − 1 (Bessel's correction), because a sample tends to understate variability. Use the population version when your data is every value in the group, and the sample version when it is a subset.
Defaults differ between tools, and so do quartile conventions, which can give slightly different values for small data sets; this page states the method it uses.
Assumptions and limitations
- Constant data gives 0
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for data set to confirm this.
Frequently asked questions
What is MAD of 1, 3, 5?
The mean of 1, 3, 5 is 3, so MAD = (2 + 0 + 2) ÷ 3 ≈ 1.33.
Is MAD in the same units as data?
Yes. Absolute deviations keep the data's units, unlike variance, which is in squared units.
Why use it?
It is intuitive and less sensitive to outliers.
What does the Mean Absolute Deviation Calculator calculate?
Average distance of values from the mean. It returns Mean absolute deviation and Mean.
What formula does the Mean Absolute Deviation Calculator use?
MAD = Σ|x − x̄| ÷ n. Mean of absolute deviations about the arithmetic mean.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Constant data gives 0.
What is an example of a mean Absolute Deviation result?
With data set 2, 4, 4, 4, 5, 5, 7, 9, the mean absolute deviation is 1.5.
Related calculators
- Mean Calculator — Mean of a data set.
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Geometric Mean Calculator — Geometric mean of a data set.
- Relative Standard Deviation Calculator — Relative standard deviation (RSD) as a percentage.
- Mean Median Mode Calculator — Mean, median and mode of a data set.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Harmonic Mean Calculator — Harmonic mean of a data set.
- Quartile Calculator — Quartiles of a data set.
- T-Score (Standardized) Calculator — Convert a raw score to a standardized T-score (mean 50, SD 10).
Sources
- Standard statistics definition (e.g. NIST/SEMATECH e-Handbook of Statistical Methods)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.