Mean Absolute Deviation Calculator
Enter your data below to get the MAD, the mean, a full step-by-step solution and a deviation graph — instantly, free, right in your browser.
Updated September 19, 2026 · Calculation method and references
Paste 2–2,000 numbers, separated by spaces, commas, tabs or newlines. Commas are separators, never thousands marks. Use decimal points; scientific notation is supported. Magnitudes: 1e-12 to 1e12, or zero. Calculations stay in this browser.
Step-by-step solution
Inspect individual deviations (25 values per page)
| # | Input | Deviation | Absolute deviation |
|---|
Absolute deviation graph
What is the mean absolute deviation?
The mean absolute deviation (MAD) measures how spread out a data set is. It is the average distance between each value and the mean: add up how far every value sits from the mean (ignoring the direction), then divide by how many values there are. A MAD of 0 means every value is identical; the bigger the MAD, the more spread out the data.
where xᵢ is each value, x̄ is the mean, and n is the number of values.
How to calculate MAD (4 steps)
- Count the values: that's your n.
- Find the mean: add all values, divide by n.
- Find each absolute deviation: subtract the mean from each value and drop the minus signs.
- Average the deviations: add them up and divide by n — that's the MAD.
Worked examples
Example 1 — test scores
Data: 3, 8, 10, 17, 24, 27
- n = 6
- Mean: x̄ = (3 + 8 + 10 + 17 + 24 + 27) / 6 = 89 / 6 ≈ 14.83
- Absolute deviations: 11.83, 6.83, 4.83, 2.17, 9.17, 12.17 → sum = 47
- MAD = 47 / 6 ≈ 7.83
Example 2 — a data set with an outlier
Data: 72, 75, 74, 73, 96, 74, 75 (daily temperatures, °F)
- Mean x̄ = 539 / 7 = 77
- Absolute deviations: 5, 2, 3, 4, 19, 3, 2 → sum = 38
- MAD = 38 / 7 ≈ 5.43
Notice the hot 96°F day: its deviation (19) is more than 2.5 × MAD ≈ 13.6, illustrating a large deviation. This comparison is descriptive, not a formal outlier test; the calculator does not classify outliers.
MAD vs. standard deviation
| MAD | Standard deviation | |
|---|---|---|
| Formula core | Average of absolute distances from the mean | Square root of the average of squared distances |
| Units | Same as the data — easy to explain | Same as the data, but less intuitive to explain |
| Outlier sensitivity | Moderate (each value counts once) | High (squaring amplifies extremes) |
| Typical use | School statistics, quick spread checks, outlier flags | Advanced statistics, finance, quality control, z-scores |
Rule of thumb: if you need to explain the spread to a human, use MAD; if you're feeding it into further statistics, standard deviation is more common.
How to interpret your MAD value
The MAD is measured in the same units as your data, which makes it easy to read: a MAD of 7.8 on test scores means "a typical score sits about 7.8 points away from the average." There is no universal "good" MAD — it only means something relative to your data's scale and to other data sets. Two comparisons help:
- Compare across data sets: two classes with the same average but MADs of 2 vs. 12 tell very different consistency stories.
- Compare to the mean itself: relative comparisons require a meaningful, nonzero mean. Do not divide by a zero or near-zero mean; a MAD near 0 indicates small absolute spread.
Some textbooks also call this the average absolute deviation or mean deviation — same calculation, different name. The median absolute deviation is different: take the median of |xᵢ − median(x)|. Simply averaging distances from the median does not produce that statistic.