Die Grundzüge der Theorie der Statistik

Abstract

THIS is an important contribution to the Calculus of Probabilities and the higher theory of Statistics. The foundation of experience on which the whole edifice of probabilities is based has been strengthened and extended by the new material which Prof. Westergaard has deposited. Here, for instance, is one of his experiments:— From a bag containing black and white balls in equal numbers, he drew (or caused to be drawn) a ball 10,000 times, the ball being replaced in the bag and the bag shaken up after each extraction. He records not only the total numbers of each colour, but also the number of white balls in each of 100 batches, each numbering 100 balls, also in 50 batches each of 200 balls, and so on. The diminution of the relative deviation from the average as the size of the batch is increased comes out clearly. On an equally large scale Prof. Westergaard has observed the proportion of prizes to blanks in batches of tickets drawn at a lottery; and the frequency with which different numbers, drawn under conditions such that one number was as likely as another, were observed to occur actually. He has similarly tabulated the frequency with which the different digits 1,2, 3, &c, terminate certain officially recorded amounts, the “kontis” of a savings bank, of which documents he has examined 10,000. These experiences afford new confirmation to the first principles of the calculus: namely, the fundamental fact of statistical regularity which the definition of probability involves, and the postulate that certain events are independent of each other in such wise that, if the probability of each be, the probability of the double event is a quarter. Die Grundzüge der Theorie der Statistik. Von Harald Westergaard, Professor an der Universität zu Kopenhagen. (Jena: Verlag von Gustav Fischer.)