The Degree of Accuracy of Statistical Data 5 



figures. Here, then, we are compelled to follow a rule which 

 ought to be more widely observed ; namely, use the degree of 

 approximation warranted by the data, and let the answer take 

 care of itself. Against this we have the contention that our data 

 are not merely three- or four-place data, but are of any desired 

 •degree of approximation, for 



'^ %yr ' 



and the division here indicated may be carried out as far as we 

 please. Further, the best theoretical curve is necessarily defined 

 as the one which fits the given observations best. Under these 

 pleas have been committed many outrageous crimes against com- 

 mon sense laws in computation, and by the greatest of masters. 

 It will be seen later, however, that a very slight change in the 

 data or even the slightest change in the unit of groupings, in 

 most cases affects the value of the moments in the third or 

 fourth place. Under these circumstances, we ought to get 

 sensibly as good a fit with three or four figures as with 

 five or six, but with only a fraction of the work. Further- 

 more, neither curve can coincide with the polygon of observa- 

 tions, and as they difter somewhat in shape, in this place the one, 

 in that the other may be the better fit. If the degree of approxi- 

 mation warranted by the data has been used, the chances are that, 

 on the whole, the one curve will be as good a fit as the other. 



To determine the degree of accuracy of the above data, I let 

 the number of cases from 15-20 years be 2018 instead of 2019, 

 a very insignificant change. Computing the v's we get: 



vi=4.294, V2:=22.343, V3=i37.072, ^4=967. 866. 

 These give for the moments about the centroid vertical 

 /i2=4-072, M3=7-595> /^4=69.347.^ 

 This change is well within the probable error of the number 

 of cases for the given period, and hence this set of values of the 



1 Had the actual distribution of the 1.3 cases above GO been in any way 

 different from the one assumed by Professor Pearson, a much greater change 

 in the moments would have occurred. 



9^ 



