Order statistics [2010]

Abstract

The test scores of students in an exam are usually ordered by the lecturer in order to overview the exam results and to evaluate the class performance. Since the exam results are not completely predictable, we admit the assumption that the test scores of students are independent and identically distributed random variables. In this case the ordered scores actually represent the realizations of the order statistics, namely ordered values of independent and identically distributed random variables. These ordered random variables play an important role in statistical theory and its applications. This article is an attempt to describe some basic notions of the theory of order statistics, their properties and applications in estimation theory and hypothesis testing. We also discuss the role of order statistics in educational statistics and provide an example of an application, the drawing up of a shortlist for the selection of students from different schools for scholarship on the basis of the ordered test scores. © 2010 Elsevier Ltd. All rights reserved.