Mean Absolute Deviation Calculator

What Is the Mean Absolute Deviation Calculator?

The Mean Absolute Deviation Calculator measures how spread out a set of numbers is. It finds the mean of your dataset, works out how far each value sits from that mean, and averages those distances. The result — the mean absolute deviation (MAD) — tells you the typical distance of a data point from the mean, in the same units as your data.

Alongside the MAD, the calculator also reports the variance and standard deviation and lists each value’s absolute deviation, so you can see exactly how the result was built up.

How to Use the Mean Absolute Deviation Calculator

1. Type your numbers into the workspace box, separated by commas — for example, 10, 20, 30, 40, 50.
2. Click Process to see the data points, the mean, the MAD, the variance, the standard deviation, and the list of absolute deviations.
3. Use Copy to copy the result, or Clear to enter a different dataset.

Worked Example

Enter the dataset 10, 20, 30, 40, 50. The calculator finds a mean of 30.0000. The absolute deviations from the mean are 20.0000, 10.0000, 0.0000, 10.0000, and 20.0000, which sum to 60. Dividing by the 5 data points gives a MAD of 12.0000. For the same dataset it also reports a variance of 200.0000 and a standard deviation of 14.1421. The formula is MAD = (Σ|x_i − x̄|) / n.

Limitations

• It describes one dataset at a time. It does not compare groups, run hypothesis tests, or say whether an observed difference is meaningful.
• The MAD is less sensitive to extreme values than the standard deviation, which is a strength for skewed data — but it also means it will not flag a single large outlier the way the variance does.
• Results are shown to four decimal places; very large datasets or values with many decimals may show rounding in the displayed figures.
• Non-numeric entries are not part of the calculation — make sure every value you enter is a number separated by a comma.

Frequently Asked Questions

What is the difference between MAD and standard deviation?

Both measure spread, but the MAD averages absolute distances from the mean, while the standard deviation averages squared distances and then takes a square root. For the example dataset, the MAD is 12.0000 and the standard deviation is 14.1421. The standard deviation gives more weight to values far from the mean.

When should I use the MAD instead of the standard deviation?

The MAD is a good choice when you want a spread measure in the original units that is not dominated by outliers, for example when summarizing typical variation in test scores or measurements with a few extreme values.

Can the MAD be zero?

Yes. If every value in the dataset is identical, each deviation is zero and the MAD is zero — there is no spread at all.

Does the calculator use the mean or the median?

This calculator uses the mean: it averages the absolute deviations from the arithmetic mean, as shown in the formula above.