In statistics, an outlier is a single observation far away from the rest of the data.
One definition of "far away" in this context is:
- less than Q1 − 1.5 × IQR or greater than Q3 + 1.5 × IQR
These values define the so-called inner fences, beyond which an observation would be labeled a mild outlier.
Extreme outliers are observations that are beyond the outer fences:
- less than Q1 − 3 × IQR or greater than Q3 + 3 × IQR
Outliers usually demand special attention since they may indicate problems in sampling or data collection or transcription. Alternatively, an outlier could be the result of, for example, a truly unusual response to a given treatment, calling for further investigation by the researcher.
See also: box plot