# Boxplot¶

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

Single Steps using the Algorithm

References

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