On the conditions under which the "probable errors" of frequency distributions have a real significance

When we seek the value of a statistical constant, we may either consider the whole aggregate of individuals possessing characteristics of which the constant in question is a function, or we may limit ourselves, from choice or necessity, to the consideration of a ramdom sample of the whole population. The mean height of Englishmen of military age, at a given instant, is a constant which could be determined from a random sample. On the other hand, the mean weight of adult herrings frequenting the North Sea is necessarily to be determined only by a consideration of a sample of the whole population. Statistical constants calculated from a sample give us little information unless we know, at the same time, the manner in which the values may be expected to vary from ramdom sample to ramdom sample,i. e . the frequency distribution of the constant in many samples. The universal custom is to state the "probable error" of the constant, which is equivalent to giving the parameter of the values of the constant in the population as a whole. The parameter-the standard deviation of the frequency distribution-therefore ceases to provide an adequate description of the facts if the frequency distribution differs sensibly from the normal.