188 REPORT— 1888. 



also be compared with otlier index-numbers upon some other objective 

 basis, such as the relative importance of each article in the import and 

 export trade of a country ; and index-numbers for one country and place 

 could be compared with those for other countries or places. The index- 

 number now suggested is only put forward as a convenient one, illus- 

 trating the variations in prices in England according to what is called 

 the standard of desiderata, and which could be made use of — not neglecting 

 others — in many investigations. 



It would also be an index-number on which, if people were so in- 

 clined, they could make contracts in a way analogous to the contracts for 

 the commutation of tithe ; in which the tithe is made to vary according 

 to the prices of corn. To make the index-number useful for this purpose 

 an Act would have to be passed prescribing the way in which the prices 

 are to be obtained and published, and defining and giving a form for the 

 contracts which might be made for payments, to vary according to the 

 variation in the aggregate index-number. This would be a practical 

 Tabular Standard such as Joseph Lowe, Jevons, and lately Professor 

 Marshall, have suggested. 



All such index-numbers are liable to the observation that innumerable 

 articles are, and must be, in the nature of things, wholly excluded. The 

 Tariety of small articles is almost infinite. The assumption may also be 

 made, I think, that on balance the permanent tendency is for such articles 

 on the average, through the progress of invention, to increase in aggregate 

 importance in proportion to the other articles which can be got into an 

 index-number and, at the same time, individually to fall relatively in 

 price. In investigations general facts of this kind would, of course, have 

 to be borne in mind as qualifying deductions based upon the precise 

 figures which the index-numbers may give. People making contracts 

 based on index-numbers would also require to study what the effect 

 ■would be likely to be on the result they wish to arrive at. 



.MEMORANDUM BV THE SECRETARY, PROFESSOR F. Y. EDGE- 

 WORTH, ON THE ACCURACY OF THE PROPOSED CALCU- 

 LATION OF INDEX-NUMBERS. 



ANALYSIS OF CONTENTS. 



Paoe 



Theoretical estimate of the discrepancj^ likely to exist between the results 

 obtained by the Committee and those which they might obtain if the 



materials were perfect 18S-198 



Practical verification and summary statement of this estimate . . . 198-201 

 Comparison of the Committee's Index-number with other schemes . . 201-210 

 "Where the data are the same for the compared methods .... 201-209 



The Simple Arithmetic Mean 201-204 



The Weighted Arithmetic Mean 204-205 



The Geometric Mean 205-206 



The Median 206-209 



Where the data are not the same for the compared methods . . 209-213 



Appendix showing the extent and significance of the difference between the 



Committee's scheme and others 213 



The usefulness of our result will be enhanced by an estimate of its 

 accuracy. It would be desirable, if possible, to ascertain a numerical 

 limit which the error ' incurred by our calculation cannot possibly, or at 



' The use of the term ' error ' to denote a deviation from an unknown ideal is 

 .somewhat infelicitous. But the advantage which the term has in being familiar to 



