XXVI 



Tables for Statisticians and Biometricians [IX — X 



and from the Table, p. 22, we have by formula (i), p. xiii : 



Tw, (4-0916) = -397,7878 + -916[3650]- 1 (-910) (-084) [1043] 

 = -398,0682. 

 Heuce Ixl^= '''^ x "398,0682 = -9978. 



Thus the odds are 9978 to 22, say 454 to 1 against a deviation-complex as 

 great as or greater than this occurring in a French male skeleton, i.e. the bones very 

 improbably were those of a Frenchman. Actually they were those of a male of 

 the Aino race. 



Illustration (ii). The following are the ordinates of a frequency distribution 

 for the speed of American trotting horses*. It is assumed that they form a 

 truncated normal curve, and we require to determine (i) the mean of the whole 

 population, (ii) its standard deviation, and (iii) what fraction the ' tail ' is of the 

 whole population. 



The values of frequency in an arbitrary scale are : 



1 Seconds 



i 



Frequency 



Seconds 



Frequency 



29— S8 



92-8 



'20—19 



45-8 



S8—27 



100-4 



19—18 



38-4 



S7—26 



95-0 



18—17 



27-8 



Z6—25 



71-2 



17—16 



19-8 



85— S4 



67-6 



16—15 



10-7 



84—23 



61-3 



15—14 



15-8 



S3— 23 



61-4 



14— IS 



7-9 



22—21 



44-8 



IS— 12 



5-0 



21—20 



44-5 



12—11 



2-1 







11—10 



5-6 



Taking the working origin at 20 — 19 seconds, wc find 



J// = -3-9214, 1// = 32-545,666 



for raw moment coefficients. Hence, if d be the distance from 29 seconds, i.e. the 



stump of the tail from the mean, and 2 the standard deviation of the tail about its 



mean : 



d =9-5- 3-9214 = 5-5786 sees., 



v-2 = „./_i,;2 = 17-168,288, 



and accordingly S7<^' = "5517. 



If this value be compared with those for ^jr^ in Table XI, p. 25, it will be seen 

 that we have got slightly more than the half of a normal curve, i.e. not a true 

 tail. We cannot therefore use Table XI, but must fall back on Table IX. 



• Gallon, E. S. Proc. Vol. 62, p. 310. See lor another method of fitting, Pearson, JUometrika, 

 Vol. II. p. 3. 



