The procedure for computing the sample circular median occasionally leads to a non-unique estimate of the population circular median, since there can sometimes be two or more diameters that divide data equally and have the same circular mean deviation. A modification in the computation of the sample median is suggested, which not only eliminates this non-uniqueness problem, but is computationally easier and faster to work with than the existing alternative.
Otieno, B. Sango and Anderson-Cook, Christine M.
"A More Efficient Way Of Obtaining A Unique Median Estimate For Circular Data,"
Journal of Modern Applied Statistical Methods: Vol. 2
, Article 15.
Available at: http://digitalcommons.wayne.edu/jmasm/vol2/iss1/15