This document explains how outliers are defined in the Exploratory Data Analysis (ED) framework (John Tukey). In a more classical setting, outliers are often defined as being values outside an interval of c units of standard deviations around the mean (often 2 or 3 standard devations)

• Estimators capable of dealing with outliers are said to be robust: the median is a robust statistic, while the mean is not.
• What to do with outliers beyond diagnosing their presence and taking appropriate steps to avoid that they unduly influence your results (violating underlying assumptions of the tool you are using) is ultimately a decision that should be based on information on the context of the data and methological and substantive considerations.
• Note that outliers are not always "true outliers", but trivial data entry errors (typos) or measurement errors, i.e. carefully checking your data is essential.

Are considered outliers all observations outside the inner fences, extreme outliers are outside the outer fences; observations between the inner and outer fences are often called "out" values, those outside the outer fences "far out" or sometimes "extremes" or "extreme outliers" and have, on a boxplot, a different marker.

• Inner fences are set at a distance of 1×step of the first and third hinge (quartile).
• Outer fences are set at a distance of 2×step of the first and third hinge (quartile).

step is defined as m×IQR (Interquartile range); m is often 1.5, sometimes 2 or 2.5.

The interquartile range is defined as

IQR =H3-H1

Where H₃ and H₁ are the third (Q³)and first quartile (Q₁)defined according to Tukey's hinges.

H3+step ≤ xi < Q3+1×step
H1-1.5×step < xi ≤ Q1+1×step

xi ≥ H3+2×step
xi ≤ H1-2×step