CXV1 



Tables for Statisticians and Biometricians [XXI XXII 



quantities differing from and 3 by considerably less than their standard errors. If 

 x represent stature, we have two sets of values for the mean and standard deviation, 



(1) for the 398 men, x = 67'4698, ^=2-6096; 



(2) for the 397 men, x' = 67'5000, o-/ = 2'5428. 



Hence for the extreme individual, who may be supposed to have had the mid-group 

 value of 55*5 inches, we find 



(1) v = (55-5 - x )/o- x = - 4-59 ; 



(2) v' = (55-5 - x')l<r x ' = - 472. 



We may now enter Table XXI with these ratios, and, using the column n = 400 as 

 sufficiently accurate, find on interpolation that the chance of drawing a sample in 



which the extreme individual is as far as or farther from the mean than this is, 

 for 



Case (1) 1 - -9991 = '0009, and Case (2) 1 - '9995 = '0005. 



It is clear that here it makes little difference whether we do or do not include the 

 extreme in calculating the mean and standard deviation, for in both cases the re- 

 sult is very exceptional, that is to say we should hesitate to consider the extreme 

 individual a random one from a "normal" population. Having discarded the in- 

 dividual with # = 55'5 inches, the extremes now lie at 59'5 and 75'5, giving 



v = (59-5 - ')/**' = - 3-15, u = (75-5 - X')/<T X ' = + 315, 



values which the table shows (for n = 400) are exceeded in about 28 / of samples. 

 By the removal of the individual with x = 55*5 inches, the sample from being 

 exceptional has become quite ordinary. 



This is as far as statistical analysis can take us ; whether or no we class the 

 man as a pathological abnormality or search for an error of record in the measure- 

 ments is beyond the province of statistical method. 



