About the Mean Absolute Deviation Calculator
The mean absolute deviation, MAD, is the average distance of the values from their mean. It is a simple measure of spread that is easier to explain than the standard deviation, because it does not square anything. This calculator also gives the median absolute deviation, which uses the median and is much less affected by extreme values. Type your numbers and the mean absolute deviation appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Mean Absolute Deviation Calculator
- 1Enter your numbers.
- 2Pick the units or options from the menus if the mean absolute deviation tool offers them.
- 3Read the mean absolute deviation in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the mean absolute deviation
Teachers use MAD to introduce spread, forecasters use the mean absolute error form to judge predictions, and analysts use the median absolute deviation as a robust scale for data with outliers.
Compare it with the standard deviation: for a normal distribution the standard deviation is about 1.25 times the mean absolute deviation. The standard deviation weights large deviations more heavily, MAD treats them in proportion.
How the mean absolute deviation is worked out
Mean absolute deviation = (|x1 − mean| + |x2 − mean| + … + |xn − mean|) ÷ n. Median absolute deviation = the median of the values |xi − median|. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the distances are 3, 1, 1, 1, 0, 0, 2, 4, which add to 12, so the mean absolute deviation is 1.5. The median is 4.5 and the median absolute deviation is 0.5.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Mean and median versions
- Shows mean and median
- Any number of values
Mistakes to avoid with mean absolute deviation
The word deviation sometimes means different things: mean absolute deviation around the mean, around the median or the median absolute deviation. This tool shows the first and the last, which are the most common. Always say which one you used when reporting results.
On phone and computer
On a phone, type into the boxes one after another and read the mean absolute deviation underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the mean absolute deviation move. The mean absolute deviation calculator works the same on both. MAD is one way to describe spread, and other measures answer slightly different questions. Compare it with the Standard Deviation Calculator, check the Variance Calculator for squared spread, and use the Outlier Calculator to find values that do not fit.
Features
- Say which MAD you use
- Median version resists outliers
- Easier to explain than SD
- Clear messages when the mean absolute deviation inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate mean absolute deviation?
Mean absolute deviation = (|x1 − mean| + |x2 − mean| + … + |xn − mean|) ÷ n. Median absolute deviation = the median of the values |xi − median|. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the distances are 3, 1, 1, 1, 0, 0, 2, 4, which add to 12, so the mean absolute deviation is 1.5. The median is 4.5 and the median absolute deviation is 0.5.
What is the formula for mean absolute deviation?
Mean absolute deviation = (|x1 − mean| + |x2 − mean| + … + |xn − mean|) ÷ n. Median absolute deviation = the median of the values |xi − median|. The mean absolute deviation calculator applies it exactly and rounds only the displayed answer to six significant figures.
Why use absolute values?
Without them the deviations above and below the mean would cancel, giving zero.
When should I use the median version?
When the data contain outliers, because they barely change the median.
How is MAD different from the standard deviation?
The standard deviation squares the deviations first, so it reacts more strongly to extreme values.
Is this mean absolute deviation calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.