On the advantage of taking the mean of a number of observations. Thomas Simpson.

On the advantage of taking the mean of a number of observations.

Publisher Information: London: Davis & Reymers, 1756.

Classic of Statistics and Data Processing

Simpson, Thomas (1710-61). On the advantage of taking the mean of a number of observations, in practical astronomy. In: Philosophical Transactions 49 (1755), pp. 82-93. Whole number, 4to. [16], 444pp. Fold. plates, text illustrations. London: L. Davis & C. Reymers, 1756. 255 x 195 mm. (uncut & unopened). Quarter morocco, marbled boards in period style. Some dust-soiling and fraying to edges, but very good.

First Edition. Simpson's paper is considered a milestone in statistical inference, as well as the earliest formal treatment of any data-processing practice. Simpson was the first to attempt to prove mathematically that the mean result of several observations is nearer to the truth than any single observation (the law of large numbers). A key feature of his paper was that Simpson chose to focus "not on the observations themselves . . . but on the errors made in the observations, on the differences between the recorded observations and the actual position of the body being observed. . . . [This] was the critical step that was to open the door to an applicable quantification of uncertainty" (Stigler, Hist. Statistics, pp. 90-91; see also pp. 88-94).

"Simpson was the first to characterize the errors in observations as independent events, taking positive and negative values with equal probabilities, and the first to provide a mathematical expression for the probability that the error in the mean result will lie between assigned limits" (Todhunter, History of Probability, p. 309).

Also present in this volume are two important medical papers: Jonathan Wathen's "A method proposed to restore the hearing, when injured from an obstruction of the tuba Eustachiana" (G-M 3356), describing his method of relieving catarrhal deafness by injections into the Eustachian tube through a catheter passed into the nose; and John Machin's "An uncommon case of a distempered skin" (G-M 4013), containing the first known description of ichthyosis hystrix.

Book Id: 35289

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