196 



EEPORT 1888. 



According to the hypotheses above made let us put c and « each 

 for the soug-ht Modulus we have 



•21. Then. 



•21 



v/378,100,000 + 4,314,200,000 



•21 X ^41 (nearly). 



l6«,yoo 



Thus the error incident to each of the data has been reduced by a half in the 

 result. It may be observed that the prices contribute much more largely thaa 

 the weights to the total error. If we reduce the error incident to each price-return 

 by a half, making its modulus •I, instead of •21, the total error of the result will 

 be reduced by nearly a half — from modulus '086 to modulus ^046. If we suppose- 

 the price-return to be quite correct, then the error of the result due to the weights- 

 alone would be nearly half as small again, namely, of modulus ^025. This is agree- 

 able to what was said above, that an error of the prices affecting only the nume- 

 rator of the index-number is not, as in the case of the weights, compensated by aa 

 error affecting the denominator in the same sense. 



Let us see now (/3) how we should have fared if we had based our estimate on the- 

 grouping of the weights and prices in prior experience. 



The dispersion of the price-returns, the coefficient C in the general formula, 

 is thus to be found — in the case of the year 1884 for example. The arithmetic 

 mean of the first nineteen entries in table"26 for 1884 is 81 nearly. The ' differ- 

 ences' and squares of differences are computed in the accompanying table. The 

 mean square of difference 353 divided by the square of the mean 6561 forms an 



approximate, a pt-imd facie value for -^ , namely, •04. 



Mean square of difference = 



6765 

 ly 



353. 



For the year 1880, taken similarly as a random specimen, the mean (of the 

 nineteen prices) is found to be 93-5, and the mean square of differences 434. 



Accordingly the value for -^ is •OS. Proceeding similarly for 1873, another year 



taken at random, we find for — - again -05. As the mean of the three values we 

 may put '05. 



