Boxplot

Local Algorithm - One-Dimensional Algorithm

Boxplot algorithm marks the lower quartile (\(Q1\)), the median (\(Q2\)), the upper quartile (\(Q3\)) of the given data set. The lower and upper inner fences are defined by \(L = Q1 - 1.5(Q3-Q1)\) and \(U = Q3 + 1.5(Q3-Q1)\). Any data value beyond the fences are treated as a value outside the region of interest.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
\(Y\)	\(Y \in \mathbb R^N\)	\(N \in \mathbb{N}\)	Input data sequence of length \(N\)

Output Parameters

Parameter	Type	Constraint	Description	Remarks
\(\hat{Y}\)	\(\hat{Y} \in \mathbb R^N\)		Values in the \(Y\) list which are outside the region of interest are marked

Tool Support

• Matlab

  For details refer to the online documentation of the function ‘boxplot’.

Single Steps using the Algorithm

• Outlier Detection with Box Plot

References

• R. McGill, J.W. Tukey, and W.A. Larsen, Variations of Boxplots, The American Statistician., vol. 32(1), pp. 12-16, 1978.