An outlier is an observation that lies outside the overall pattern of a distribution (Moore and McCabe 1999). Usually, the presence of an outlier indicates some sort of problem. This can be a case which does not fit the model under study, or an error in measurement.


Outliers are often easy to spot in histograms. For example, the point on the far left in the above figure is an outlier.

A convenient definition of an outlier is a point which falls more than 1.5 times the interquartile range above the third quartile or below the first quartile.


Outliers can also occur when comparing relationships between two sets of data. Outliers of this type can be easily identified on a scatter diagram.

When performing least squares fitting to data, it is often best to discard outliers before computing the line of best fit. This is particularly true of outliers along the x direction, since these points may greatly influence the result.

See also

Histogram, Least Squares Fitting, Scatter Diagram Explore this topic in the MathWorld classroom

This entry contributed by John Renze

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Moore, D. S. and McCabe, G. P. Introduction to the Practice of Statistics, 3rd ed. New York: W. H. Freeman, 1999.

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Cite this as:

Renze, John. "Outlier." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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