cxiv Tables for Statisticians and Biometricians [XXI XXII 



The constants of the frequency distribution of u (or v), as determined by 

 equation (1) on p. ex, are provided in the following table, absolute values being 

 in terms of the standard deviation of the sampled population as unit. 



Constants of the Distribution of the Largest Individual in Samples 

 from a Normal Population. 



It is interesting to note that we have here an example of a statistical variate 

 the distribution of which diverges more from normality as the sample increases in 

 size. The accompanying Diagrams 2, 3 and 4 (pp. cxii cxiii) will enable the 

 student to estimate roughly, in the case of a sample not appearing in the above 

 table, the values of the standard deviation, /3 X and /3 2 - 



From fa = to & = '326 (or /3 2 = 3 to 3'594) the approximate curve of distribu- 

 tion is a Type IV curve. That is to say, the largest or smallest individual frequency 

 extends indefinitely in both directions. When & = '326, ft z = 3'594 or with samples 

 of about 36 the frequency is represented by a Type V curve, passing into a Type VI. 

 Thus in these cases the frequency is limited, or the chance that the largest in- 

 dividual will be one showing a large negative deviation is vanishingly small as we 

 increase the size of our samples to 36 or more individuals. This is the physical 

 interpretation of our passing to curves which have theoretically a finite limit to the 

 frequency. The accompanying Diagram 5 in conjunction with the table indicates 

 the type of curve which may be selected to represent the frequencies of samples 

 of various sizes. 



Illustration. The table on p. cxvi gives the distribution of stature among 398 

 men, aged 36'0 39*0, measured at Galton's Anthropometric Laboratory at South 

 Kensington in 1884*. It will be seen that there is one exceptional individual with 

 a stature of about 4 ft. 7 ins. The distribution of stature (for adults) is known to 

 be approximately represented by the normal curve, and in fact if we omit the 

 exceptional case the remaining 397 individuals give 



fa = 3-0947, 



* The figures have been extracted from Table I of the paper by Buger and Stoessiger, Annals of 

 Eugenics, Vol. n. 1927, p. 91. 



