Mean Absolute Deviation Calculator
A plain-English measure of spread — the average distance your numbers sit from their mean — computed from your list along with the mean itself.
How it works
First the calculator finds the mean of your list. Then it measures how far each value sits from that mean, ignoring whether it's above or below by taking the absolute value, and averages those distances.
Because it uses absolute distances rather than squared ones, the mean absolute deviation stays in the same units as your data and reads as a straightforward 'on average, values are this far from the middle.'
Take 3, 6, 6, 7, 8, 11, 15, 16. The mean is 9, the absolute distances are 6, 3, 3, 2, 1, 2, 6, 7, and their average is 3.75 — so a typical value sits about 3.75 away from the mean.
Frequently asked questions
How is this different from standard deviation?
Both measure spread, but MAD averages the plain distances from the mean while standard deviation averages the squared distances and then takes a root. MAD is easier to explain and less swayed by extreme outliers, since it doesn't square the big gaps.
Why take the absolute value at all?
Without it, the distances above the mean would cancel the ones below and the total would always come out to zero. Stripping the signs keeps every distance positive so they add up into a meaningful average.
What does a small MAD tell me?
A small mean absolute deviation means your values cluster tightly around the mean — the data is consistent. A large one signals wide scatter. Comparing the MAD to the mean itself gives a quick feel for how variable the numbers are.
Can MAD be measured from the median instead?
It can, and some fields prefer deviation from the median because it's even more robust to outliers. This calculator uses the mean, which is the version most commonly taught and the one usually meant by 'mean absolute deviation.'