Median Absolute Deviation Calculator

For Mean Absolute Deviation, go to Mean absolute deviation calculator

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What is MAD?

In statistics, MAD may be the acronym for Median Absolute Deviation or Mean Absolute Deviation

What is Median Absolute Deviation?

The Median Absolute Deviation (MAD), is a statistic that measures the data variability.
The MAD is the average absolute distances from the arithmetic mean.
It is similar to the standard deviation, but instead of the addition of squares differences, it uses the absolute differences, and obviously, there is no need to take a square root.

Median Absolute Deviation formula (MAD formula)

MAD = Median(|Xi - Mdn|)
Mdn = Median(Xi)
MAD = Median(|Xi - Median(Xi)|)

Should I use Mean Absolute Deviation or Median Absolute Deviation?

The question is similar to the question "Should I use average or median?".
Both average and median measure the data variability Usually, we use the average statistic.
We prefer the Median Absolute Deviation in one of the following cases:
1. The data contains outliers.
2. The data is very skewed, and the sample size is not large
In these cases, one outlier or one rare extreme value might change the data variability dramatically.
The median is not affected by extreme values.