Exact Bounds on Finite Populations of Interval Data

In this paper, we start research into using intervals to bound the impact of bounded measurement errors on the computation of bounds on finite population parameters (“descriptive statistics”). Specifically, we provide a feasible (quadratic time) algorithm for computing the lower bound σ on the finite population variance function of interval data. We prove that the problem of computing the upper bound σ2 is, in general, NP-hard. We provide a feasible algorithm that computes σ2 under reasonable easily verifiable conditions, and provide preliminary results on computing other functions of finite populations.