APPENDIX III. 307 



case and adding one year at the other end. In this way 

 individual fluctuations are eliminated, and the general trend 

 of the movement ascertained. Particularly interesting were 

 the results found by this means in movements in yield of 

 wheat compared with acreage. 



The average used in all calculations was the simple 

 arithmetic average. Such an average is simple, easy of 

 calculation, applicable to any set of numbers, and lends 

 itself to further statistical work. Despite the disadvantages 

 arising from the fact that it is greatly influenced by extremes, 

 and may be inaccurate if the data are incomplete, it is, 

 probably, the most convenient average for calculating the 

 index numbers necessary for this investigation. 



In Table XXVII., the index numbers of the prices of 

 English and New Zealand wheat have been compared for the 

 purposes of ascertaining which series is subject to the greatest 

 and most frequent fluctuations. The methods used are 

 explained briefly in the text,* but it may be stated here 

 that changes in prices or other economic phenomena involve 

 many considerations. There are (1) the frequency of change 

 which may be observed best in a graph; (2) the average 

 range of change which is calculated by the simple average 

 of the individual movements; (3) the range of change, which 

 is the difference between the smallest and greatest items in 

 the series; and (4) the average of departures from the average, 

 which is a measure to some extent of the degree of the 

 fluctuations. The devices used to measure these changes in 

 the case of the prices of English and New Zealand wheat are 

 given in the text, and are of particular importance to the 

 problem of price steadiness. 



But it is not intended to discuss the whole problem of 

 index numbers. The treatment given here is altogether in- 

 complete from this point of view. It is hoped, however, that 

 it will prove useful to those who are unfamiliar with index 

 numbers. For a fuller treatment reference should be made to 

 any of the following works: 



Mcllraith : The Course of Prices in New Zealand. 



Fisher : The Purchasing Power of Money. 



Lay ton : An Introduction to the Study of Prices. 



*See page 181, 



