Mean Absolute Deviation Calculator
Average distance from the mean, in the original units.
Enter your values
Enter the data values you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Mean absolute deviation
- 3.75
- MAD about the median
- 3.5
- Mean
- 9
- Standard deviation
- 4.5981
- Deviations
- 6, 3, 3, 2, 1, 2, 6, 7
- MAD ÷ SD ratio
- 0.816
Quick answer
Mean absolute deviation is the average of the absolute distances from the mean, giving a spread measure in the same units as the data.
MAD = Σ|xᵢ − x̄| ÷ n
At a glance
| What it does | Average distance from the mean, in the original units. |
|---|---|
| Category | Statistics |
| Inputs needed | Data values |
| Main output | Mean absolute deviation |
| Formula | MAD = Σ|xᵢ − x̄| ÷ n |
| Cost | Free — no sign-up, no download |
How to use the Mean Absolute Deviation Calculator
- 1Enter your data values.
- 2Read the MAD — it is the typical distance from the mean.
- 3Compare with the standard deviation; for normal data the ratio sits near 0.8.
Inputs explained
- Data values
- Enter the data values you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- Data values3, 6, 6, 7, 8, 11, 15, 16
Results
- Mean absolute deviation3.75
- MAD about the median3.5
- Mean9
- Standard deviation4.5981
- Deviations6, 3, 3, 2, 1, 2, 6, 7
- MAD ÷ SD ratio0.816
Frequently asked questions
MAD or standard deviation?
MAD is easier to explain and less swayed by outliers. Standard deviation feeds into most formal statistics, so both have a place.
Why absolute values?
Without them the deviations cancel to exactly zero, which tells you nothing about spread.
What do I need to enter into the Mean Absolute Deviation Calculator?
Just 1 value: data values. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Mean Absolute Deviation Calculator work out the answer?
Mean absolute deviation is the average of the absolute distances from the mean, giving a spread measure in the same units as the data. It applies the formula MAD = Σ|xᵢ − x̄| ÷ n and shows the working so you can check each step by hand.
Is the Mean Absolute Deviation Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.