Foutentheorie en wiskundige statistiek

Physicists and chemists hardly ever use the standard deviation for expressing the errors of their observations. This is attributed to the facts that the error theory as commonly treated in textbooks on physics is based too exclusively on the normal frequency distribution, and leaves some of the most important practical problems unanswered. The main advantage of mean and standard deviation lies in the very simple mathematical relations satisfied by these quantities regardless of the shape of the frequency distribution. These relations are discussed in the first part of this paper, while in the second part they are employed for a thorough treatment of the degree of rounding off permissible in practice. The following rules of thumb are derived: The maximum permissible rounding interval should be (A) one half of the standard deviation, or (B) one sixth of the range computed from 5 to 10 observations, or (C) one sixth of the maximum mutual difference observed in ten pairs of observations. The rounding interval should be at least one fifth of the maximum just specified. In setting up these limits the following principles were adopted: (1) that the changes in the mean and the standard deviation produced by rounding off must not be too large, and (2) that rounding off must be productive of an effective simplification in the numerical treatment of the data, in particular in the computation of the standard deviation.