It is pertinent to inquire what are the limits of variation in terms of standard use in respect to human intelligence. How far superior to the average person are the most highly intelligent individuals currently produced? Galton's (9) X grade of man was defined in terms of incidence as "one in a million." But this X man was not a product of one variable. Galton's X man resulted from an intellect _in combination_ with "zeal and power of working." The incidence of this _combination_ of traits would probably be less than the incidence of intellect alone in degree sufficient for X.
Our purpose in this chapter will be to consider investigations, made by direct methods, of the origin and development of children of a type extremely rare in occurrence, incidence being based on one variable only; i.e., intelligence measured in terms of IQ (S-B). For this purpose the line might be drawn at any point farther than +7 PE or +8 PE from the mean. A choice of 180 IQ (S-B) as a minimum insures a degree of plus deviation very rarely found even in metropolitan cities and their suburbs, as is clear from the reports of mental surveys conducted during the present century. The choice of 180 IQ (S-B), instead of 179 or 181 or some other amount of IQ in the extreme upper range, is obviously arbitrary and is adopted merely for the purpose of defining a point at and above which there are very few children who score.
_Frequency of occurrence_. Just how often does a child testing above 180 IQ (S-B) appear in the juvenile population of the United States? We cannot tell exactly until we know more about the spread of the distribution of IQ (S-B). In terms of PE (1 PE = ±8 IQ), according to Terman's original findings (24) we should come upon a deviate of +10 PE only once in more than a million times, provided the distribution of IQ corresponds exactly or even rather closely to Quetelet's (17) curve of probability as respects spread; for on this curve cases above or below ±5 PE approach zero in frequency.
It is certain, however, even from existing data, that the distribution of IQ extends for at least ±10 PE (even assuming that wider data will define 1 PE as ±10 instead of ±8 as found by Terman. It is probable that children who test above 180 IQ are actually present in our juvenile population in greater frequency than at the rate of one in a million. This does not mean that intellect when finally measured _in true units_ may not conform in variability to the mathematics of chance; it means only _in terms of IQ_ (in terms of ratio and not of absolute units) the conformity is probably not exact, as respects the law of deviation.
