Mean Absolute Deviation Calculator
Find the mean absolute deviation (MAD) of a list of numbers, with each value's distance from the mean.
Change the values and press Calculate to work out your own figures.
Enter numbers to find their average distance from the mean.
| Value | |x − mean| |
|---|---|
| 10 | 12.25 |
| 2 | 20.25 |
| 38 | 15.75 |
| 23 | 0.75 |
| 38 | 15.75 |
| 23 | 0.75 |
| 21 | 1.25 |
| 23 | 0.75 |
Show the working
- Mean = 22.25
- Σ|x − mean| = 67.5
- MAD = 67.5 ÷ 8 = 8.4375
How to use it
Enter numbers to find their average distance from the mean.
Paste or type the numbers separated by commas, spaces or new lines. Results are worked out exactly and shown to 12 significant figures; Show the working lists each step.
Key facts
MAD = Σ|x − mean| ÷ n
MAD or standard deviation?
MAD averages the distances themselves, so it is easier to explain; the standard deviation squares them, which weights large deviations more heavily.
Questions
How do I find the MAD?
Find the mean, take each value's distance from it, and average those distances.
Is this the median absolute deviation?
No; this is the mean absolute deviation around the mean.
Formulas
MAD = Σ|x − mean| ÷ n
Sources
Limitations
- Up to 5,000 values. Values are separated by commas, spaces or new lines, so write 1250 rather than 1,250.