46 Mr. F. Galton on Statistics by Intercomparison. 



The latter also comprises 1024 events ; but it is made up of 

 three parts : viz. nine tenths of it are due to a 10-element series ; 

 and of the remaining tenth, half are due to a 9 and half to an 

 11 series. I have reduced all these to the proper ratios, ignoring 

 fractions. It will be observed how close is the correspondence 

 between the compound and the simple series. 



Total cases. 



Number of 

 elements. 



Successive grades in the series. 



1. 



2. 



3. 



4. 



5. 



6. 



7. 



8. 



9. 



10. 



11. 



12. 



52 

 924 



48 



9 



10 

 11 





 1 

 



1 

 9 

 



4 

 41 



1 



8 



108 



4 



13 



189 

 8 



13 



227 



11 



8 



189 



11 



4 



108 



8 



1 



41 



4 





 9 

 1 





 1 

 





 

 



1024 

 1024 



Compound series. 

 10 



1 10 

 1 10 



46 

 45 



120210251 

 120210252 



208 

 210 



120 

 120 



46 

 45 



10 

 10 



1 



1 









 



0~ 





Difference 







+ 1 







0|_, 



-2 







+ 1 







It appears to me, from the consideration of many series, that 

 the want of symmetry commonly observed in the statistics of 

 vital phenomena is mainly due to the inclusion of small series 

 of the above character, formed by alien elements ; also that the 

 disproportionate number of extreme cases, as of giants, is due to 

 this cause. 



The general conclusion we are justified in drawing appears 

 to be, that, while each statistical series must be judged accord- 

 ing to its peculiarities, a law of frequency of error founded 

 on a binomial ogive is much more likely to be approximately 

 true of it than any other that can be specified a priori ; also 

 that the exponential law is so closely alike in its results to those 

 derived from the binomial ogive, under the circumstances and 

 within the limits between which statisticians are concerned, that 

 it may safely be used as hitherto, its many well-known proper- 

 ties being very convenient in all cases where it is approximately 

 true. Therefore, if we adopt any uniform system (such as already 

 suggested) of denoting the magnitudes of qualities for the mea- 

 surement of which no scale of equal parts exists, such system 

 may reasonably be based on an inverse application of the law 

 of frequency of error, in the way I have described, to statis- 

 tical series obtained by the process of intercomparison. 



