Mean Absolute Deviation Calculator

Enter a data set to compute its mean absolute deviation — the average distance of each value from the mean — using MAD = (1/n)·Σ|xᵢ − mean|, with the full working shown.

Quick Facts

Formula
MAD = (1/n)·Σ|xᵢ − x̄|
Average absolute distance of each value from the mean, in the data's own units.

Your Results

Calculated
Mean absolute deviation
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MAD = (1/n)·Σ|xᵢ − mean|
Mean (x̄)
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Arithmetic average of the data
Count (n)
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Number of data points
Sum of |deviations|
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Σ|xᵢ − mean| (before dividing by n)

Ready

Enter your data set and click Calculate.

What is mean absolute deviation?

The mean absolute deviation (MAD) of a data set is the average distance between each value and the mean of the set. It answers a simple question: "on average, how far are my data points from their center?" Because it is expressed in the same units as the original data, MAD is one of the most intuitive ways to describe how spread out a set of numbers is.

The formula

For a data set x₁, x₂, …, xₙ with mean x̄:

MAD = (1/n) · Σ |xᵢ − x̄|

In words: compute the mean, subtract it from every value, take the absolute value of each difference (so negative and positive deviations do not cancel), add those absolute deviations together, and divide by the number of points, n.

Worked example

Take the data set 4, 8, 6, 5, 3, 10, 9, 7 (n = 8). The sum is 52, so the mean is 52 ÷ 8 = 6.5. The absolute deviations from 6.5 are 2.5, 1.5, 0.5, 1.5, 3.5, 3.5, 2.5, 0.5, which add up to 16. Dividing by 8 gives MAD = 16 ÷ 8 = 2. So on average each value sits 2 units away from the mean of 6.5.

MAD vs. standard deviation

Both statistics measure spread, but they treat deviations differently. Standard deviation squares each deviation, averages the squares, and takes a square root — which magnifies large deviations and makes it sensitive to outliers. MAD simply averages the raw absolute deviations, so it is more robust and easier to explain. For data drawn from a normal distribution the two are related by MAD ≈ 0.7979 × standard deviation (that constant is √(2/π)). MAD is never larger than the standard deviation for the same data.

Why use MAD?

  • Interpretability: it is a plain average distance, in the data's own units — no squaring or square roots to explain.
  • Robustness: it is less inflated by a single extreme value than standard deviation or variance.
  • Teaching: it is commonly introduced in middle- and high-school statistics as a first measure of variability before variance and standard deviation.

Frequently Asked Questions

What is mean absolute deviation?
Mean absolute deviation (MAD) is the average distance of each data point from the mean of the set. You compute the mean, take the absolute value of each point's deviation from that mean, and average those absolute deviations: MAD = (1/n)·Σ|xᵢ − mean|. It measures spread in the same units as the data.
How is MAD different from standard deviation?
Both measure spread, but MAD averages the absolute deviations while standard deviation averages the squared deviations and then takes a square root. Standard deviation weights large deviations more heavily and is more sensitive to outliers; MAD is more robust and easier to interpret. For a normal distribution, MAD ≈ 0.7979 × standard deviation.
Does MAD use the mean or the median?
This calculator computes deviations about the arithmetic mean, which is the standard "mean absolute deviation." A related measure, the median absolute deviation, takes deviations about the median instead and is even more resistant to outliers. They are different statistics — make sure you know which one your assignment or report requires.
Can MAD be zero or negative?
MAD is zero only when every value in the set is identical (there is no spread). It can never be negative, because it averages absolute values, which are always zero or positive.

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