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Walk-through

How to Use This Calculator

5 steps

1

Enter your data set

Type your numbers into the Data values field, separated by commas, spaces, or new lines — for example 2, 4, 6, 8, 10. The calculator updates instantly as you type.

2

Choose mean or median

Pick Mean for the standard MAD calculation, or Median if you want a measure that's more resistant to outliers. Both use the same data set — only the center point being measured from changes.

3

Read the MAD result

The result card shows the mean absolute deviation, the center value used, and how many data points were included. The interpretation line explains the spread in plain language.

4

Compare mean vs median

Switch to the About Mean/Median tab to see MAD about the mean and MAD about the median side by side for the same data — useful for spotting how much outliers are inflating the mean-based figure.

5

Check the deviations table

The Deviations tab lists every value alongside its signed deviation and absolute deviation from the chosen center, plus the summary line showing exactly how the average was calculated — so you can verify the math by hand.

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Reference

Formula & Methodology

3 formulas

Mean absolute deviation

MAD = (sum of |x - center|) / n

Find each value's distance from the center (ignoring sign), add up all those distances, then divide by the number of values.

Center — mean

mean = (sum of all x) / n

The default center point: the arithmetic average of the data set.

Center — median

median = middle value (or average of the two middle values)

An alternative center point that resists distortion from outliers, since it depends only on rank order, not magnitude.

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Glossary

Key Terms Explained

6 terms

Mean absolute deviation The average distance between each value in a data set and a chosen center point (the mean or median), calculated by averaging the absolute values of the deviations.

Average deviation Another name for mean absolute deviation — the two terms are used interchangeably in most statistics texts.

Mean The arithmetic average of a data set — add up every value and divide by how many there are.

Median The middle value of a data set once sorted in order (or the average of the two middle values, for an even count). Unlike the mean, it isn't pulled toward extreme values.

Dispersion A general term for how spread out a data set is. Mean absolute deviation, variance, standard deviation, and range are all measures of dispersion.

Absolute value The non-negative magnitude of a number, written |x|. It strips the sign so that a deviation of -3 and a deviation of +3 both contribute equally to the average, instead of canceling out.

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Scenarios

Real-World Examples

3 worked examples

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Textbook check

Small data set, MAD about the mean

Data 2, 4, 6 About Mean

The mean is 4, and the absolute deviations are 2, 0, and 2. Summing those gives 4, and dividing by n = 3 gives a mean absolute deviation of 1.33 — each value sits about 1.33 units from the mean of 4 on average.

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Same data, MAD about the median

Data set with an outlier, both centers compared

Data 1, 2, 3, 4, 10 About Mean vs Median

The mean is 4, giving a MAD of 2.4. The median is 3, giving a MAD of 2.2 — smaller, because the median (3) sits closer to the bulk of the data than the mean (4), which the single large value of 10 pulls upward. This is the classic case for preferring MAD about the median when outliers are present.

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MAD vs standard deviation

Comparing dispersion measures on the same data

Data 4, 8, 6, 5, 3, 7 About Mean

MAD averages the absolute distances from the mean without squaring them, so a single large deviation affects the result less than it would in a variance or standard deviation calculation. For data with occasional extreme values, MAD often gives a more intuitive sense of "typical" spread.

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Deep Dive

Understanding Mean Absolute Deviation (MAD)

3 chapters · 4 min read

Mean absolute deviation is one of the simplest ways to describe how spread out a data set is — take every value's distance from the center, average those distances, and you have a single number that answers "how far do values typically sit from the middle?" It's easier to compute by hand and easier to interpret than variance or standard deviation, which is why it's often introduced first in statistics courses.

How MAD is calculated

MAD starts the same way variance does: pick a center point (the mean, most commonly) and measure how far every value sits from it. But instead of squaring each deviation, MAD takes the absolute value — stripping the sign so a value 3 below the center and a value 3 above it both count as a distance of 3, without one canceling the other out. Those absolute deviations are then averaged: sum them all up and divide by the number of data points. The result is expressed in the same units as the original data, with no need for a separate square-root step like standard deviation requires.

MAD about the mean vs MAD about the median

Most textbook definitions measure MAD about the mean, but measuring about the median is a valid and sometimes more useful alternative. Because the median depends only on rank order rather than magnitude, it doesn't shift much when an extreme value is added to the data set — while the mean can be pulled substantially toward that outlier. As a result, MAD about the median is more robust: it tends to give a smaller, more representative figure for data sets that include occasional extreme values, while MAD about the mean can end up inflated by the very outlier it's trying to describe.

MAD vs standard deviation

Both MAD and standard deviation measure dispersion, but they treat large deviations differently. Standard deviation squares every deviation before averaging, which means a value far from the center contributes disproportionately more to the final number — a single outlier can dominate the whole calculation. MAD only takes the absolute value, so a large deviation still counts more than a small one, but not nearly as dramatically. This makes MAD a gentler, more outlier-resistant summary of spread, at the cost of some of the convenient mathematical properties (like its relationship to the normal distribution) that make standard deviation the default choice in most formal statistical work.

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Questions

Frequently Asked Questions

6 questions

What is the formula for mean absolute deviation?+

MAD is the mean of the absolute deviations: find the mean or median of the data, subtract it from each value, take the absolute value of each result, then average those absolute deviations. In symbols: MAD = (sum of |x − center|) / n.

What does the 'about the median' option do?+

It changes the center point the deviations are measured from — instead of the mean, each value's distance is measured from the median. The median is generally more resistant to outliers, so MAD about the median can give a smaller, more representative figure when the data set contains extreme values.

How is MAD different from standard deviation?+

Standard deviation squares each deviation before averaging (then takes a square root at the end), which weights large deviations much more heavily. MAD simply takes the absolute value of each deviation, so it's less sensitive to outliers and easier to compute and interpret by hand.

What units does mean absolute deviation use?+

The same units as the original data. If your values are measured in dollars, MAD is in dollars; if they're measured in seconds, MAD is in seconds — unlike variance, which is in squared units.

When is mean absolute deviation zero?+

MAD is zero only when every value in the data set is identical to the chosen center — in other words, when there's no spread at all.

Is mean absolute deviation more robust than standard deviation?+

Yes, generally. Because MAD only takes the absolute value of each deviation rather than squaring it, a single extreme value has less influence on the final result than it would on variance or standard deviation, making MAD a more robust — though less commonly used in formal statistics — measure of spread.

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Mean Absolute Deviation Calculator

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