Introduction

Abstract

In earlier works on statistics, and especially in German books on Kollektivmaßlehre, the concepts of frequency, mean, standard deviation, etc., were developed for the case of fixed finite collections only, and attention was restricted entirely to that case. On the other hand, English and American statisticians considered any set of statistical data to be a random sample from an infinite collection, or population, of possibilities. From this point of view, the frequency of an event is only an estimate of the corresponding probability of the event, and the sample mean is only an estimate of the population mean, or expectation. The central question of statistics then becomes: by how much can the quantities calculated for the random sample differ from the corresponding quantities for the population? Thus, today, we have come to base mathematical statistics on the theory of probability.