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Mean Absolute Deviation Calculator
Your numbers
Example: 2, 4, 6, 8, 10 → mean 6, MAD 2.4.
Behind the numbers
How mean absolute deviation is calculated
The mean absolute deviation (MAD) measures the average distance of the numbers from their mean. First find the mean by adding all the numbers and dividing by how many there are. Then find the absolute deviation of each number — how far it is from the mean, ignoring whether it is above or below. Add those distances up and divide by the number of values. That average distance is the MAD.
Worked example — data 2, 4, 6, 8, 10. Mean = (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6. Absolute deviations from 6: |2 − 6| = 4, |4 − 6| = 2, |6 − 6| = 0, |8 − 6| = 2, |10 − 6| = 4. Sum = 4 + 2 + 0 + 2 + 4 = 12. MAD = 12 ÷ 5 = 2.4.
Examples
Examples
| Data | Mean | MAD |
|---|---|---|
| 2, 4, 6, 8, 10 | 6 | 2.40 |
| 1, 2, 3, 4, 5 | 3 | 1.20 |
| 10, 20, 30 | 20 | 6.67 |
| 2, 4, 4, 4, 5, 5, 7, 9 | 5 | 1.50 |
| 5, 5, 5, 5 | 5 | 0.00 |
Tips before you use it
MAD uses absolute values, so a number below the mean counts the same as one the same distance above it.
A MAD of 0 means every number is the same — there is no spread at all.
MAD is in the same units as your data: if your numbers are test scores, the MAD is in points.
Unlike standard deviation, MAD does not square anything, so one very large outlier changes it less.
Use MAD when you want a simple, easy-to-explain measure of spread; use standard deviation when your class or textbook asks for it.
Good to know
Frequently asked questions
What does a MAD of 2.4 mean?
It means the numbers are, on average, 2.4 units away from their mean. A small MAD means the numbers cluster close to the mean; a large MAD means they are widely spread out.
What is the difference between MAD and standard deviation?
Both measure spread around the mean. MAD averages the absolute distances, while standard deviation averages the squared distances and then takes a square root. Standard deviation gives extra weight to numbers far from the mean; MAD treats all distances equally.
Can MAD be negative?
No. Absolute deviations are never negative, so their average is always zero or positive. A MAD of zero means all the numbers are identical.
When is MAD used instead of standard deviation?
MAD is common in school math and in simple data summaries because it is easy to explain and to calculate by hand. It is also handy when a data set has outliers, since it is less affected by them than standard deviation.