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Mean Absolute Deviation Calculator

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Mean Absolute Deviation Calculator

The mean absolute deviation (MAD) is the average distance between each value and the mean of the data. It answers the question “how far from the average is a typical value?” without squaring, so it is the first measure of spread most students meet, and it is a common topic in Grade 6–8 and GCSE statistics.

Enter your numbers and the calculator finds the mean, lists every deviation, takes absolute values, adds them up and divides by the count. The table it produces is the same one you would draw by hand. The median absolute deviation (distance from the median, then the median of those distances) is reported as well, since some courses use that definition.

Compared with the standard deviation, the MAD gives less weight to extreme values. For a normal distribution the MAD is about 0.8 times the standard deviation, so if you know one you can estimate the other, but for skewed data the ratio can be quite different.

Separate values with commas, spaces or new lines.

Result and step-by-step solution

Mean absolute deviation
2.25

On average, each value is 2.25 away from the mean of 12.75. (Median absolute deviation about the median: 2.)

  1. Mean
    x̄ = 102 ÷ 8 = 12.75
  2. Absolute deviations
    xx − x̄|x − x̄|
    10−2.752.75
    12−0.750.75
    152.252.25
    9−3.753.75
    141.251.25
    185.255.25
    11−1.751.75
    130.250.25
  3. Sum of absolute deviations
    Σ|x − x̄| = 18
  4. Divide by n
    MAD = 18 ÷ 8 = 2.25

Frequently asked questions

How do you calculate mean absolute deviation?
Find the mean, subtract it from each value, drop the minus signs, add the results and divide by the number of values.
What does a mean absolute deviation of 5 mean?
On average, each data value is 5 units away from the mean. A smaller MAD means the values cluster more tightly.
Is MAD the same as standard deviation?
No. The SD squares the deviations before averaging and then takes a square root, which gives extreme values more influence. The two are related but not equal.
Does MAD sometimes mean median absolute deviation?
Yes, especially in robust statistics. This page reports both: the mean absolute deviation is the main result and the median absolute deviation is shown underneath.

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Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.

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