Mean Absolute Deviation Calculator Formula

Understand the math behind the mean absolute deviation calculator. Each variable explained with a worked example.

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Formulas Used

Mean Absolute Deviation

mad = (abs(v1 - mn) + abs(v2 - mn) + abs(v3 - mn) + abs(v4 - mn)) / 4

Mean

mean_val = mn

Variables

VariableDescriptionDefault
v1Value 13
v2Value 26
v3Value 39
v4Value 412
mnDerived value= (v1 + v2 + v3 + v4) / 4calculated

How It Works

How to Calculate Mean Absolute Deviation

Formula

MAD = (1/n) * Sum of xi - mean

For each value, find the absolute difference from the mean, then average those differences. Unlike variance, MAD does not square the deviations, making it less sensitive to outliers and easier to interpret: it is literally the average distance from the mean.

Worked Example

Find the MAD of 3, 6, 9, 12.

v1 = 3v2 = 6v3 = 9v4 = 12
  1. 01Mean = (3 + 6 + 9 + 12) / 4 = 30 / 4 = 7.5
  2. 02Absolute deviations: |3-7.5|=4.5, |6-7.5|=1.5, |9-7.5|=1.5, |12-7.5|=4.5
  3. 03Sum of absolute deviations = 4.5 + 1.5 + 1.5 + 4.5 = 12
  4. 04MAD = 12 / 4 = 3

Frequently Asked Questions

How does MAD differ from standard deviation?

MAD uses absolute deviations while SD uses squared deviations. MAD is more robust to outliers and easier to interpret, but SD has nicer mathematical properties for theoretical statistics.

Is MAD always smaller than standard deviation?

For most distributions, yes. For a normal distribution, MAD ≈ 0.7979 * SD. Squaring in SD amplifies large deviations, making SD generally larger.

When should I use MAD?

Use MAD when you want a robust, easily interpretable measure of spread, especially if outliers are present or the distribution is non-normal.

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