Ixvi Tables for Statisticians and Biometricians [XXXV — XLVI 



The working origiu was taken at 20, the ceutre of the group 18 — 22. The 

 centre of the first group at 1-47 % is »-(20- r47) = 3-706 on the negative side of 

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



Percentage 



Frequency 



Percentage 



Freijuency 



0— 3* 



15 



J,3-47 



45 



.•?— 7 



120 



1,8-53 



24 



S—]2 



139 



53—57 



14 



IS— 17 



157 



5S—02 



6 



1S—S2 



158 



63—67 



3 



'2S—27 



139 



68—72 



3 



28—32 



117 



7S — 7 /"" 



2 



33—37 



92 



78—82 



2 



38-1,2 



50 



83—87 



— 



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

 being 5 ^, the raw moment coefficients are : 



v,'= -567,2191, v.,'= 7-703,4990, 

 V,' = 28-982,5042, v,' = 253-268,8780. 

 Whence transferring to mean and correcting, we have 



Mean = 22-8361, o-= 2-70156, 

 /i, = 7-298,428, /Li3 = 16-238,780, /X4 = 198-909,921. 



These lead to 



/3i = -678,295, /3, = 3-734,202, 



K, = 2/3„ - 3A - 6 = - -566,483, k, = - 1-052,180, 

 sk = -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 : 



0- = 13-5078 and rf = 6-6875. 



We can now find the probable errors of those constants. We first want %i 

 from Table V, but 1086 is outside the limit of n. We therefore take x-, foi' 543 

 and have Xi = '02047, and we find x^ = '014,47. We can repeat our constants with 

 their probable errors 



Mean = 22-8861 ± -2765, a = 135078 ± -1955. 

 Then from Table XXXVII, 



^, = 3-7 : \/FS^. = 4-70 + If? [2] = 4-71, 

 /3, = 3-8: V:WSp, = 5-05+§§a[2] = 5-06. 



Hence for /3, = 3-7342 : ViVSp, = 4-71 + f^ljV [35], 



ViVSp, = 4-83. 

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



