APPENDIX III. 307 
ease 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:— 
MclIiraith : The Course of Prices in New Zealand. 
Fisher: The Purchasing Power of Money. 
Layton: An Introduction to the Study of Prices. 
*See page 181, 
