MihsabaShare this free calculator
Send this tool to someone who needs the calculation.
How to use
This calculator finds mean absolute deviation: the average absolute distance between values and a chosen center. Use the mean, median or a custom center. Because deviations are not squared, the result stays in the same units as the data.
- Enter the dataset.
- Choose mean, median or a custom center.
- Calculate to see MAD and descriptive values.
How it is calculated
Example
Example: for 4, 8, 6, 5, 3, 7, the mean is 5.5 and absolute distances sum to 9, so MAD = 9 / 6 = 1.5.
Important notes
MAD can also mean median absolute deviation, which is a different statistic. This tool computes the mean of absolute deviations around the selected center.
Worked examples and interpreting results
For data 2, 4, 6, the mean centre is 4. Absolute deviations are 2, 0, 2, averaging about 1.3333.
| Case | Calculation | Result |
|---|---|---|
| Centre | (2 + 4 + 6) ÷ 3 | 4 |
| Mean absolute deviation | (|2 − 4| + |4 − 4| + |6 − 4|) ÷ 3 | 1.333333 |
How to check the result
Select mean centre. The result averages absolute deviations from the selected centre; choosing median centre does not turn the operation into median absolute deviation.
Frequently asked questions
Is MAD less sensitive to outliers than variance?
Often yes because deviations are not squared, though outliers can still affect the mean and mean-centered MAD.
Can I measure around the median?
Yes. Select median as the center.
What units does MAD use?
The same units as the input data.
Is deviation about the mean the same as deviation about the median?
No. Absolute deviations can be computed around different centers and give different results. Mean absolute deviation uses the arithmetic mean here, while the median minimizes total absolute deviation and is more robust to outliers.