Mean Absolute Deviation Calculator
This mean absolute deviation calculator finds the average distance of your values from their mean or median. Example: for 2, 4, 4, 4, 5, 5, 7, 9 the MAD around the mean is 1.5.
Source: Wikipedia – Average absolute deviation. Updated: .
How it is calculated
The mean absolute deviation (MAD) tells you how far the values in a list lie from their centre on average. Unlike the standard deviation, the distances are not squared; their absolute values are averaged instead.
Formula and steps
First pick the centre c: usually the mean, or the median for skewed data. Then take |x − c| for every value, add all these distances and divide by the count n: MAD = Σ|x − c| / n. There is no n − 1 correction here.
Worked example
The values 2, 4, 4, 4, 5, 5, 7, 9 have a mean of 5. The absolute distances are 3, 1, 1, 1, 0, 0, 2 and 4, which add up to 12. Divided by n = 8 this gives MAD = 1.5. Measured from the median 4.5 instead, the distances also add up to 12, so MAD = 1.5 again. With other data the two versions usually differ.
- The MAD is never larger than the standard deviation; here the population standard deviation is 2.
- The median as centre gives the smallest MAD of all possible reference points.
Frequently asked questions
How do you calculate the mean absolute deviation?
Find the mean, take the absolute difference of each value from it, add those distances and divide by the number of values.
How is MAD different from standard deviation?
The standard deviation squares the distances and takes a root at the end, so large deviations weigh more. The MAD averages the absolute distances directly and is easier to interpret.
Should I measure around the mean or the median?
Both are used. For symmetric data the results are close; with outliers the median is more robust. A textbook task usually means the mean.
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