Let x1x2 ··· xn be any set of number satisfying Σ xi=0 Σ xi2=1. There are bounds on the range of xi when the set xi is ranked (a) by x1≥x2≥ ··· ≥ xn and (b) by x1≥x2≥ ··· ≥xn. These bounds are given. The applicability to finite populotionr is pointed out. © Taylor & Francis Group, LLC.