# Statistics and Probability Dictionary

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### Outlier

In regression analysis, a data point that diverges greatly from the overall pattern of data is called an outlier.

In more general usage, an outlier is an extreme value that differs greatly from other values in a set of values. As a "rule of thumb", an extreme value is considered to be an outlier if it is at least 1.5 interquartile ranges below the first quartile (Q1), or at least 1.5 interquartile ranges above the third quartile (Q3).

To illustrate, consider the following example. Suppose we sample 10 households and note the annual income of each household. Suppose we find that nine of the households have incomes between \$20,000 and \$100,000; but the tenth household has an annual income of \$1,000,000,000. That tenth household is an outlier.

The figure below shows a distribution with an outlier. Except for one lonely observation (the outlier on the extreme right), all of the other observations appear on the left side of the distribution.

 0 1 2 3 4 5 6 7 8 9
Outlier on right
 See also: AP Statistics Tutorial: Graphical Display of Data | AP Statistics Tutorial: Influential Points