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*

*Q1*and

*Q3*are the first and third quartiles, respectively, and

*IQR*is the interquartile range (equal to

*Q3*−

*Q1*).

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