Mean Absolute Deviation Calculator

Mean absolute deviation (MAD) calculator for checking how spread out your numbers are

Mean absolute deviation, usually shortened to MAD, is a simple way to measure how much your numbers vary around their average. If your values cluster tightly around the mean, MAD will be small. If values are spread out, MAD will be larger. People commonly search for MAD when they need a quick, understandable measure of variability without jumping straight to variance or standard deviation.

This calculator is locked to one job: compute mean absolute deviation around the mean for a single list of numeric values. It is useful for quick checks like comparing the consistency of two sets of measurements, checking whether a small dataset has a lot of fluctuation, or summarising how far values typically sit from the average. It does not calculate median absolute deviation (a different statistic) and it does not attempt to handle grouped frequency tables.

To use it, paste your values into the input field using spaces, commas, or new lines as separators. Then click “Calculate MAD”. The results section shows the mean, the MAD, and a small set of supporting figures that make the MAD easier to interpret. If you enable the deviation breakdown option, you will also see each value and its absolute deviation from the mean, which helps you spot which values are driving the variability.

Assumptions and how to use this calculator

• MAD is calculated around the arithmetic mean (average), not around the median.
• Your input is treated as a simple list of numbers, with each value counted once.
• Separators can be commas, spaces, or new lines. Commas inside a number are not supported because commas are treated as separators.
• All values can be negative, zero, or positive. MAD is always reported as a non-negative amount in the same units as your data.
• The calculator uses a straightforward average of absolute deviations (sum of absolute deviations divided by the number of values). No “sample vs population” adjustment is applied because MAD does not use that correction.

Common questions

What does mean absolute deviation tell me in plain language?

MAD tells you the typical distance of your values from the mean. For example, if MAD is 2.50, then values are typically about 2.50 units away from the average. It is easier to interpret than variance because it stays in the same units as the data.

Is mean absolute deviation the same as standard deviation?

No. Both measure spread, but they are calculated differently. Standard deviation squares deviations and is more sensitive to large outliers. MAD uses absolute values, which tends to be more robust and easier to explain. If you are working with methods that require standard deviation (like many statistical formulas), MAD is not a direct substitute.

Can I use this for negative numbers or values around zero?

Yes. The mean can be negative or near zero, and MAD still works because it uses absolute deviations. If the mean is exactly zero, a “relative MAD” percentage is not meaningful, so the calculator will omit that percentage output.

Why does the calculator warn about using commas in large numbers?

Because commas are treated as separators between values. If you enter 1,000 it will be read as two values: 1 and 000. If you need to enter thousands, type 1000. If you need decimals, use a dot, like 1000.50.

How can I improve the accuracy or usefulness of the result?

Accuracy comes from data quality, not extra settings. Make sure you include all relevant observations, avoid mixing units, and check for typos. If you want interpretability, turn on the deviation breakdown to see which specific values are far from the mean, then decide whether those values are valid measurements or errors.