[124] For fuller information see a paper on "The Estimation of Minute Quantities of Gold," by Dr. George Tate; read before the Liverpool Polytechnic Society, Nov. 1889.
[125] Journal of the Society of Chemical Industry, No 4, vol. ix. April 30, 1890.
APPENDIX C.
A LECTURE ON THE THEORY OF SAMPLING.
The problem of the sampler is essentially the same as that of the student of statistics. One aims at getting a small parcel of ore, the other a number of data, but each hopes to obtain what shall represent a true average applicable to a much larger mass of material. Ignoring the mechanical part of the problems, the sampling errors of the one and the deviations from the average of the other are the same thing.
It may be doubted whether many not specially trained in the study of statistics could answer such a question as the following:—Seven hundred thousand men being employed, there are, in a given year, one thousand deaths from accident. Assuming the conditions to remain unaltered, within what limits could one foretell the number of deaths by accident in any other year?
On the other hand, there is a widespread belief in the efficacy of what is called the law of averages. Even the ordinary newspaper reader is accustomed to look on the national death-rate or birth-rate as a thing capable of being stated with accuracy to one or two places of decimals, and he knows that the annual number of suicides is practically constant.
If a man played whist often and kept a record of the number of trumps n each hand, he would find fortune treated him quite fairly; in a year's play the average number would deviate very little from the theoretical average, i.e., one-quarter of thirteen. And a knowledge of this truth is useful, and that not merely in keeping ejaculations in due restraint. But every good player knows more than this: he has a sense of what variations in the number of trumps may reasonably be expected. For example, he will be prepared to risk something on neither of his opponents having more than five trumps, and will accept it as a practical certainty that no one has more than eight. Much of what is known as good judgment is based on a proper estimate of deviations from the average. The question has an important bearing on sampling, as may be seen from the fact that shuffling and dealing at cards are but modifications of the well-known mixing and quartering of the sampler.