# Outlier

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Definition
 Outlier A rare, atypical observation. A data value that is numerically distant from the rest of the data. The presence of an outlier may indicate some sort of problem -- possibly a data error or a data value which is fundamentally different from the other data.

Tip: Identifying outliers...

There is no universally-agreed-on criterion for defining an outlier, however using $1.5\,$ times the interquartile range (IQR) to identify data values substantially below the first quartile (Q1) or above the third quartile (Q3) provides a good rule of thumb. With this rule an observation is considered a suspected outlier if it is:

• below $\ Q1 - 1.5(IQR)\,$
• above $\ Q3 + 1.5(IQR)\,$

Regardless of your method for identifying outliers, always assess the effects of outliers on the statistical conclusions.

## Examples

The histogram shown below displays a dataset with one high outlier - a value between 75 and 80, with the next highest value between 50 and 55.

# Web Resources

 Hayden, Robert W. (2005). "A Dataset that is 44% Outliers." Journal of Statistics Education. 13(1). High, Robin. (2000). Dealing with 'Outliers:' How to Maintain Your Data's Integrity. Computing News. University of Oregon.

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