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how to find mean absolute deviation

To find the mean absolute deviation (MAD), you follow a simple three-step process: find the mean, find each distance from the mean, then average those distances.

How to Find Mean Absolute Deviation

Quick Scoop

Mean absolute deviation tells you, on average, how far the data values are from the mean. It’s a way of measuring how “spread out” a dataset is.

Step-by-step method (MAD from the mean)

Suppose your data set is: 4, 7, 9, 10, 16.

  1. Find the mean (average).
    • Add all values: 4+7+9+10+16=464+7+9+10+16=464+7+9+10+16=46.
    • Divide by the number of values (5): 46÷5=9.246÷5=9.246÷5=9.2.
      So the mean is 9.2.

  1. Find each absolute deviation from the mean.
    Subtract the mean from each data point and ignore negative signs (take absolute value):

    • ∣4−9.2∣=5.2|4−9.2|=5.2∣4−9.2∣=5.2
    • ∣7−9.2∣=2.2|7−9.2|=2.2∣7−9.2∣=2.2
    • ∣9−9.2∣=0.2|9−9.2|=0.2∣9−9.2∣=0.2
    • ∣10−9.2∣=0.8|10−9.2|=0.8∣10−9.2∣=0.8
    • ∣16−9.2∣=6.8|16−9.2|=6.8∣16−9.2∣=6.8
      These are the absolute deviations.
  1. Find the mean of those absolute deviations.
    • Add them: 5.2+2.2+0.2+0.8+6.8=15.25.2+2.2+0.2+0.8+6.8=15.25.2+2.2+0.2+0.8+6.8=15.2.
    • Divide by 5: 15.2÷5=3.0415.2÷5=3.0415.2÷5=3.04.
      So the mean absolute deviation of this data set is 3.04.

In words:

MAD = average of the distances of each data point from the mean.

The general MAD formula

If your data values are x1,x2,…,xnx_1,x_2,…,x_nx1​,x2​,…,xn​ and their mean is μ\mu μ, then

MAD=1n∑i=1n∣xi−μ∣\text{MAD}=\frac{1}{n}\sum_{i=1}^{n}|x_i-\mu|MAD=n1​i=1∑n​∣xi​−μ∣

This just encodes the same steps: subtract mean, take absolute value, add them all, divide by how many there are.

What MAD tells you (intuitively)

  • A small MAD means values are usually close to the mean (data is tightly clustered).
  • A large MAD means values are often far from the mean (data is more spread out).

For example, a class where test scores all sit near 80 will have a smaller MAD than a class where some scores are near 40 and some near 100.

Quick checklist you can memorize

  1. Find the mean of the data.
  1. Subtract the mean from each value, take absolute value.
  1. Average those absolute values → that’s the mean absolute deviation.

You can also compute MAD in many spreadsheets or calculators; for example, some spreadsheet programs have a function similar to AVEDEV that returns the mean absolute deviation for a list of numbers.

TL;DR:
Mean absolute deviation = “average distance from the mean”: find the mean, find each distance from it (ignoring minus signs), then average those distances.

Information gathered from public forums or data available on the internet and portrayed here.