NEW BOUNDS FOR THE EXTREME VALUES OF A FINITE-SAMPLE OF REAL NUMBERS

We derive new bounds for the smallest value x(min) and the largest val ue x(max) of a finite sample x(1),...,x(n) of real numbers. Our bounds are obtained by solving two optimization problems, one of them being convex and the other nonconvex. We show that the pair (x(min), x(max)) lies in a region bounded by an ellipse and an hyperbola. The correspo nding cartesian equations are given in terms of the average and the st andard deviation of the sample. (C) 1996 Academic Press, Inc.