[discrete]
[[esql-agg-median-absolute-deviation]]
=== `MEDIAN_ABSOLUTE_DEVIATION`
The median absolute deviation, a measure of variability. It is a robust
statistic, meaning that it is useful for describing data that may have outliers,
or may not be normally distributed. For such data it can be more descriptive than
standard deviation.

It is calculated as the median of each data point’s deviation from the median of
the entire sample. That is, for a random variable `X`, the median absolute deviation
is `median(|median(X) - Xi|)`.

[source.merge.styled,esql]
----
include::{esql-specs}/stats_percentile.csv-spec[tag=median-absolute-deviation]
----
[%header.monospaced.styled,format=dsv,separator=|]
|===
include::{esql-specs}/stats_percentile.csv-spec[tag=median-absolute-deviation-result]
|===

NOTE: Like <<esql-agg-percentile>>, `MEDIAN_ABSOLUTE_DEVIATION` is
      <<esql-agg-percentile-approximate,usually approximate>>.

[WARNING]
====
`MEDIAN_ABSOLUTE_DEVIATION` is also {wikipedia}/Nondeterministic_algorithm[non-deterministic].
This means you can get slightly different results using the same data.
====