Studies in the History of Probability and Statistics: VII. The Principle of the Arithmetic Mean

The history of the problem of combining a set of independent observations on the same quantity is traced from antiquity to the appearance in the eighteenth century of the arithmetic mean as a statistical concept. The problem of estimating parameters from observational data appears first to have presented itself to the Babylonian astronomers of the last three centuries B.C. Their achieve-ments are recorded in cuneiform script on clay tablets and have been analysed by Neuge-bauer (1951) who has also (1955) published a collection of the texts. The following summary is abstracted from his researches. Between about 500 and 300 B.C., the Babylonians developed a systematic mathematical theory to account for the motions of the sun, moon and planets; and they evolved simple arithmetical schemes by which the positions of these bodies could be calculated at regular intervals of time. Beyond the fact that the basic parameters in the schemes represent a compromise between observation and the needs of computation, nothing has survived to indicate how they were estimated from the original data, which are themselves almost wholly absent. Rather more information is available concerning the methods by which the Gree