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.