How to calculate mean absolute deviation
The mean absolute deviation (MAD) is the average of how far each value sits from the mean, using absolute values. Find the mean, take the absolute difference of each value from it, then average those differences. For 2, 4, 4, 4, 5, 5 the mean is 4 and the deviations are 2, 0, 0, 0, 1, 1, summing to 4, so MAD = 4 ÷ 6 ≈ 0.667. Squaring the deviations instead of taking their absolute value leads to the standard deviation calculator, which is why the two rarely agree.
How to use this calculator
Enter your numbers and leave unused fields blank. The result is the MAD, rounded to three decimals, with the mean and count shown alongside. For a squared-deviation measure, compare with the variance calculator.
MAD vs. standard deviation
Both measure spread, but MAD uses absolute distances while standard deviation uses squared distances, so standard deviation reacts more strongly to outliers. MAD is easier to interpret because it stays in the original units. To find the middle value instead, use the median calculator.
Frequently asked questions
- How do I calculate the mean absolute deviation?
- Find the mean, take the absolute difference of each value from it, then average those differences. For 2, 4, 4, 4, 5, 5 the MAD is 0.667.
- Is MAD the same as standard deviation?
- No. MAD averages absolute deviations; standard deviation uses squared deviations, making it more sensitive to outliers.
- Why use absolute values?
- Without absolute values the positive and negative deviations cancel out and the average would be zero.
- Does a blank field count?
- No. Only the values you enter are used in the mean and the MAD.
- What does a MAD of zero tell me?
- It means every value in the data set is identical, so no value sits any distance from the mean. MAD can never be negative, and the larger it grows relative to the mean itself, the more scattered the data is around its centre.