Mean Absolute Deviation Calculator
Enter a list of numbers to find the mean absolute deviation (MAD), the average distance of each value from the mean, with every step shown.
Mean absolute deviation formula
MAD = Σ|x − mean| ÷ n
- Find the mean of the data.
- Subtract the mean from each value and drop any minus signs.
- Average those absolute deviations.
Worked example
For 2, 4, 6, 8, 10 the mean is 6. The absolute deviations are 4, 2, 0, 2, 4, which add up to 12. MAD = 12 ÷ 5 = 2.4.
MAD vs standard deviation
Both measure spread. MAD uses absolute values, so it is easier to interpret and less affected by outliers. Standard deviation squares the deviations, giving extra weight to large ones.
Frequently asked questions
What does MAD tell you?
On average, how far the values are from the mean. A small MAD means the data are tightly grouped.
Can MAD be negative?
No. It is an average of absolute values, so it is always zero or positive.
Is MAD the same as median absolute deviation?
No. Median absolute deviation uses medians instead of means. The calculator shows the mean deviation about the median as an extra row.
When is MAD zero?
Only when every value is the same.
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