In Hoare's (1961) original version of the algorithm
the partitioning element in the central divide-and-conquer
step is chosen uniformly at random from the set S in question.
Here we consider a variant where this element is the median
of a sample of size 2k+1 from S. We investigate convergence
in distribution of the number of comparisons required and obtain
a simple explicit result for the limiting
average performance of the median-of-three version.