Computational Statistics

, Volume 27, Issue 3, pp 381–392 | Cite as

Boxplot for circular variables

  • Ali H. Abuzaid
  • Ibrahim B. Mohamed
  • Abdul G. Hussin
Original Paper


A boxplot is a simple and flexible graphical tool which has been widely used in exploratory data analysis. One of its main applications is to identify extreme values and outliers in a univariate data set. While the boxplot is useful for a real line data set, it is not suitable for a circular data set due to the fact that there is no natural ordering of circular observations. In this paper, we propose a boxplot version for a circular data set, called the circular boxplot. The problem of finding the appropriate circular boxplot criterion of the form ν × CIQR, where CIQR is the circular interquartile range and ν is the resistant constant, is investigated through a simulation study. As might be expected, we find that the choice of ν depends on the value of the concentration parameter κ. Another simulation study is done to investigate the performance of the circular boxplot in detecting a single outlier. Our results show that the circular boxplot performs better when both the value of κ and the sample size are larger. We develop a visual display for the circular boxplot in S-Plus and illustrate its application using two real circular data sets.


Circular boxplot Boxplot Resistant constant Outlier Overlapping 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Ali H. Abuzaid
    • 1
  • Ibrahim B. Mohamed
    • 1
  • Abdul G. Hussin
    • 2
  1. 1.Institute of Mathematical SciencesUniversity of MalayaKuala LumpurMalaysia
  2. 2.Center for Foundation Studies in ScienceUniversity of MalayaKuala LumpurMalaysia

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