lxvi Tables for Statisticians and Biometricians [XXXV — XLVI 



The working origin was taken at 20, the centre of the group 18 — 22. The 

 centre of the first group at 1*47 % is i(20 - ]-47) = 3706 on the negative side of 

 the working origin and may be taken to contribute — 56, + 206, — 763, + 2830 



to the first, second, third and fourth moments respectively. The working unit 

 being 5 °/ o , the raw moment coefficients arc : 



vfm -567,2191, ■/,'« 7703,4990, 



v,' = 28-982,5042, vl = 253-268,8730. 



Whence transferring to mean and correcting, we have 



Mean = 228361, a = 270156, 



^,-7*298,428, fi 3 = 16-238,780,. ^=198-909,921. 



These lead to 



ft - -678,295, ft = 37 34,202, 



«, = 2ft - 3/3, - 6 = - -566,483, k, = - 1-052,180, 



tk = 495,087, Distance from Mean to Mode = d = 1-337,508. 



These values, except the mean, are all in working units. Therefore in per- 

 centages of black : 



a= 13-5078 and d = 6-6875. 



We can now find the probable errors of these constants. We first want ^, 

 from Table V, but 1086 is outside the limit of n. We therefore take ^ 2 for 543 

 and have ^ = -02047, and we find ^ 2 = -014,47. We can repeat our constants with 

 their probable errors 



Mean = 228361 ± 2765,- a = 135078 ± -1955. 

 Then from Table XXXVII, 



ft = 3-7: ^2,, = 4-70 + !$$[2] = 4-71, 



ft = 3-8 : ViV2 ft = 5-05 + f§§ [2] = 5-06. 



Hence for ft = 37342 : >JN2 $< = 4-71 + f$& [35], 



V J r 2 ft = 4-83. 

 * 4 at and 11 at 2, giving a mean at 1-47 %. 



