Outlier

What it does to each measure

Compare these two sets, identical except for the last value:

Data	Mean	Median	Range	IQR
$5, 6, 6, 7, 7, 8, 9$	$6.9$	$7$	$4$	$2$
$5, 6, 6, 7, 7, 8, 94$	$19$	$7$	$89$	$2$

The mean nearly triples and the range grows more than twentyfold. The median and interquartile range do not move at all.

That split is the practical point. Measures built from every value — the mean and mean absolute deviation — feel an outlier strongly. Measures built from positions — the median and IQR — barely notice one.

Spotting one

A dot plot shows an outlier immediately as a lone dot away from the cluster.

Without a picture, a large gap between the range and the IQR is the signature. A set whose middle half spans $4$ and whose full range is $60$ has something far out in a tail.

An outlier is not automatically an error

Sometimes it is a typo — a height recorded as $1750$ cm rather than $175$. Then it should be corrected.

Often it is real and is the most interesting value in the set. One unusually long hospital stay, one component that failed early, one exceptional result: these are genuine observations, and deleting them because they are inconvenient changes what the data says.

The honest response is to report a measure of center that is not distorted by it, and to say the outlier is there.