Suppose that a finite set E, a family of feasible subsets of E and a real cost associated with each element in E are given. This paper considers the problem of finding a feasible subset such that the variance of the costs of elements in the subset is minimum among all feasible subsets. The case is considered in which the number of elements in a feasible subset is a constant, i.e., it does not depend on the choice of the subset. This paper first exhibits a parameteric characterization of an optimal solution of the above minimum variance problem. Based on this characterization, it is shown that if one can solve in polynomial time the problem of finding a feasible subset that minimizes the sum of costs in the subset, it is possible to construct a fully polynomial time approximation scheme for the above minimum variance problem.
