Mean Absolute Deviation Calculator
Paste your numbers and get the mean absolute deviation: the average distance between your values and their mean.
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Find the mean absolute deviation
Separate with spaces, commas or new lines.
| Value | Value − mean | Distance |
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Show the working
How to calculate mean absolute deviation
Find the mean
Add the values and divide by how many there are. For 2, 4, 6, 8 the mean is 20 ÷ 4 = 5.
Measure each distance
Subtract the mean from each value and drop the minus sign: 3, 1, 1, 3.
Average the distances
(3 + 1 + 1 + 3) ÷ 4 = 2. The mean absolute deviation is 2.
Dropping the minus signs is the whole trick. Without it the distances always cancel out to zero, which is why the standard deviation squares them instead.
Questions people ask
What is mean absolute deviation?
The average distance between each value and the mean. A small MAD means the values are bunched together; a large one means they are spread out.
How is MAD different from standard deviation?
Both measure spread. MAD averages the plain distances from the mean; standard deviation squares them first, averages, then takes the square root. Squaring makes the standard deviation react more strongly to values far from the mean, so it is usually the larger of the two.
Why do you drop the minus signs?
Because the signed differences from the mean always add up to exactly zero, so their average would be zero for every data set. Taking the absolute value keeps each distance positive so the average means something.
Can the MAD be zero?
Yes, and only when every value is identical. There is no spread, so every distance from the mean is zero.
Does this divide by n or n − 1?
By n, the full count. The n − 1 adjustment belongs to the sample standard deviation and variance, not to mean absolute deviation.
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