The Frequency Distribution of the Unknown Mean of a Sampled Universe

V E R Y observation or series of observations upon the items composing a "universe" or " p o p u l a t i o n " m a y be regarded as constituting a sample. We m a y divide sampling into two broad natural classes, (1) Sampling of Attributes, and (2) Sampling of Variables. The theory of the first class concerns itself with some particular characteristic, such as the color red, which each item of the universe definitely does or does not possess, and endeavors to assign, ultimately, a numerical value to the probability that the number or proportion of the items in the universe having this characteristic lies within any given range. The second division comprehends that wide variety of problems in which each item of the universe displays to a greater or less degree the same particular quality, such as length, weight, or resistance. After having drawn a random sample of items, probability theory is called upon to assert with what likelihood certain important descriptive constants or " p a r a m e t e r s " of the universe lie within any given ranges. In either class the problem is legitimately attacked by means of a posteriori probability theory. This theory makes use of the two important distinct kinds of knowledge which, in varying amounts, are always at hand, namely, (1) a priori or preexisting information regarding the universe and the possible values which the unknown 632 A METHOD OF SAMPLING INSPECTION 631 values of zmIn., k, and (c, a) in equation (1') and solving for M. If, for this value of M thus found, the selected values of c and a coincide with those read respectively from Figs.