Mean Absolute Deviation Calculator
Find the mean absolute deviation (MAD) of a data set.
Results update as you type.
About this calculator
The mean absolute deviation (MAD) is the average distance between each value and the mean, using absolute values so distances never cancel out. It measures spread like the standard deviation but is simpler and less sensitive to outliers, because it does not square the deviations. This calculator reports the MAD together with the mean, range and the sum of absolute deviations it was measured from.
The method is direct: find the mean, take the absolute value of each value’s distance from it, add those distances up and divide by the number of values. Because it averages plain distances rather than squared ones, the MAD is expressed in the original units and is easy to explain to a non-technical audience.
Worked example: for 2, 4, 6, 8, 10 the mean is 6. The absolute deviations are 4, 2, 0, 2, 4, which sum to 12, so the MAD is 12 ÷ 5 = 2.4 — on average each value sits 2.4 units from the mean. The deviation table below lists every value’s distance so you can trace the result.
Frequently asked questions
How is MAD different from standard deviation?
MAD averages the absolute deviations, while standard deviation averages the squared deviations and then takes a square root. Because it does not square, MAD gives less weight to outliers and is often easier to explain, but standard deviation has more convenient mathematical properties.
How do I calculate MAD by hand?
Find the mean, subtract it from each value and take the absolute value of every result, then average those distances. For 2, 4, 6, 8, 10 the mean is 6 and the MAD is (4+2+0+2+4)/5 = 2.4.
Is mean absolute deviation the same as mean deviation?
Yes, the two terms usually refer to the same thing: the average of the absolute distances from a central point, most often the mean. Some textbooks measure the distances from the median instead, which minimises the total distance, but this calculator uses the mean.
Why does MAD use absolute values?
Deviations above the mean are positive and those below are negative, and they always sum to zero, so their plain average is useless. Taking the absolute value strips the sign so every distance counts, giving a genuine measure of spread.
When should I prefer MAD over standard deviation?
Choose MAD when you want a spread measure that is easy to explain and robust to outliers, or when squaring would over-weight a few extreme values. Standard deviation is preferred when you need the mathematical properties it feeds into, such as the normal distribution or variance-based tests.
Can the mean absolute deviation be zero?
Only when every value equals the mean — that is, when all the numbers are identical and there is no spread. Otherwise the MAD is always a positive number.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/mean-absolute-deviation/curl
curl "https://calculator.free/api/v1/mean-absolute-deviation/?numbers=2, 4, 6, 8, 10"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/mean-absolute-deviation/?" + new URLSearchParams({
"numbers": "2, 4, 6, 8, 10"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.