Each individual partakes of this racial psychology as he does of many other mental unions, such as his church and his political party; but that which has pre-eminence in history and psychology is not these, but that closer and paramount union to which he is bound by a common speech, ideas, motives, and hopes. We must not forget, however, that under whatever connotation we understand the group, it is still composed of individuals; and the relations which these bear to it require careful consideration. The unity of a group can never be complete. The infinite variations of its individual members prevent this. And here comes in an interesting law which has lately been defined by an American scientist. He has shown that precisely that trait or those traits which are the most distinguishing characteristics of a group vary the widest in the individuals of that group. Let us take, for instance, a given community remarkable for the average height of its members. We shall find wider variations in this dimension among them than among a community less conspicuous in this measurement. This appears to hold equally good for the statistics of longevity, of health and disease, and other physical traits. There is little doubt it is also of general application to mental qualities. The contradictory estimates of national character largely depend upon it. Not the bias of the observers but their ignorance of the operation of this law will often explain such discrepancies. What method should we follow to avoid such an error? In other words, what formula can we devise to correct individual variation and arrive at a true average for the group? This work has already been done for us. Diligent students of vital statistics have as good as demonstrated that when a given characteristic of a group can be expressed in numbers and these projected by the graphic method, the resultant curve obtained will be one of those called by mathematicians binomial. Subtracting from the whole number one-tenth for aberrant forms or abnormal cases (the distribution of error), of the remainder, one-half will represent the mean, and one-fourth each will represent the plus and minus extremes. For example, suppose in a given community numbering one thousand adults the average height is 5 feet 6 inches; in it, one hundred persons (one-tenth) will be either abnormally tall or short; of the remainder, 450 will attain just about the total average height; while 225 will be above and 225 below it. We can fearlessly adopt this method of reasoning in ethnic psychology. When we speak of mental traits or ideas common to the group, we mean that they may be held as expressed by scarcely half of that group; that in the remainder of the group they may be much more positively adopted or more or less rejected; but inasmuch as such numerous exceptions largely annul each other’s force, the general tendency and action of the group will be guided by the average rather than by either extreme.