Mean absolute deviation

Mean absolute deviation is the average distance of each observation from the mean, using absolute values instead of squares, giving a spread measure in the data's original units.

ByHoang TruongUpdated July 5, 2026

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A café's daily sales over five days average 48 units. Each day's absolute distance from that mean is 8, 7, 13, 12 and 2 units, summing to 42. Dividing by the five observations gives a mean absolute deviation of 8.4 units — daily sales typically differ from the average day by about 8.4 units.

Where it fits

TopicDescriptive StatisticsCoreSubjectData Analysis & StatisticsCore

The formula

LaTeX

\text{MAD} = \frac{1}{n}\sum_{i=1}^{n} \left| x_i - \bar{x} \right|

Variables

$x_{i}$: Value of observation i
$\overset{x}{ˉ}$: Sample mean
$n$: Number of observations in the sample (observations)

Average of the absolute distances of each observation from the sample mean; always divided by n, the number of observations.

Check yourself

PracticeCORE

Weekly overtime hours for 4 employees are: 10, 4, 8, and 2. What is the mean absolute deviation of these hours?

Select an answer to check your understanding.