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Calculation Machine

Mean Absolute Deviation Calculator

Average distance from the mean, in the original units.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Mean absolute deviation
3.75
MAD about the median
3.5
Mean
9
Standard deviation
4.5981
Deviations
6, 3, 3, 2, 1, 2, 6, 7
MAD ÷ SD ratio
0.816

Quick answer

Mean absolute deviation is the average of the absolute distances from the mean, giving a spread measure in the same units as the data.

The formula

MAD = Σ|xᵢ − x̄| ÷ n

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Data values3, 6, 6, 7, 8, 11, 15, 16

Result

  • Mean absolute deviation3.75
  • MAD about the median3.5
  • Mean9
  • Standard deviation4.5981
  • Deviations6, 3, 3, 2, 1, 2, 6, 7
  • MAD ÷ SD ratio0.816

How to use the Mean Absolute Deviation Calculator

  1. 1Enter your data values.
  2. 2Read the MAD — it is the typical distance from the mean.
  3. 3Compare with the standard deviation; for normal data the ratio sits near 0.8.

Frequently asked questions

MAD or standard deviation?

MAD is easier to explain and less swayed by outliers. Standard deviation feeds into most formal statistics, so both have a place.

Why absolute values?

Without them the deviations cancel to exactly zero, which tells you nothing about spread.

About this calculator