Introduction. In Chapter II we have dealt to some extent with the effects of random sampling fluctuations on relative frequencies. But it is fairly obvious that the interest of the statistician in the effects of sampling fluctuations extends far beyond the fluctuations in relative frequencies. To illustrate, suppose we calculate any statistical measure such as an arithmetic mean, median, standard deviation, correlation coefficient, or parameter of a frequency function from the actual frequencies given by a sample of data. If we need then either to form a judgment as to the stability of such results from sample to sample or to use the results in drawing inferences about the sampled population, the common-sense process of induction involved is much aided by a knowledge of the general order of magnitude of the sampling discrepancies which may reasonably be expected because of the limited size of the sample from which we have calculated our statistical measures.

We may very easily illustrate the nature of the more common problems of sampling by considering the determination of certain characteristics of a race of men. For example, suppose we wish to describe any character such as height, weight, or other measurable attributes among the white males age 30 in the race. We should almost surely attempt merely to construct our science on the basis of results obtained from the sample.