APPENDIX III. 



THE CALCULATION AND USE OF INDEX NUMBERS. 



Index numbers are used most frequently to measure changes 

 in general or individual prices, but they have certain advantages 

 for measuring other economic phenomena. The most simple 

 use has been made of index numbers in this work and it will 

 not be necessary to state all the problems to which they give rise. 

 For in all cases changes in only individual prices or other 

 phenomena have been measured, and thus it is not necessary 

 to discuss the important question of sampling in its relation 

 to the choice of commodities. 



The method of calculating an index number can best be 

 stated by reference to a particular instance of its use. The 

 index numbers of prices of New Zealand wheat will be 

 considered.* First it is necessary to choose a period of years 

 (or a single year) as a base period with which to compare 

 the prices in all other years. The base period should be one 

 in which no abnormal circumstances have been at work. Such 

 a period is found in the years 1890-99, which have been taken 

 as the base in all the calculations. These years are particu- 

 larly appropriate, for they contain a period of falling prices 

 to 1895 and then rising prices to 1899. The average of the 

 period is then calculated. In the particular case under con- 

 sideration the average price of New Zealand wheat from 1890 

 to 1899 was 3s. 5d. per bushel. This was equated to 100 and 

 then the corresponding numbers found for the prices year by 

 year, with this equation as a basis. Thus in 1869 the average 

 price of New Zealand wheat was 4s. 3d. per bushel. The 

 index number for this year would be 124. It is then an easy 

 matter to calculate the percentage change from the base 

 period. In a similar way index numbers have been found 

 for other phenomena, e.g., supplies of wheat from year to 

 year, area in wheat, imports, exports, etc. These index 

 numbers offer many advantages, for they are often more 

 convenient to work with than the original figures, which may 

 be unwieldy, or, or the contrary, too small. Comparisons 

 between two series can much more readily be undertaken, and 

 the index numbers are useful for the purposes of drawing 

 graphs, especially where two sets of data have to be compared 

 graphically. Further, in calculating the general trend of the 

 changes in the phenomena index numbers are very useful. The 

 general trend has been found by calculating decennial moving 

 averages. Suppose that the index numbers commence in 1869, 

 then the moving average is ascertained in the following manner. 

 Find the average of the years 1869-78, then of the years 

 1870-79, then 1871-80, and so on, dropping one year in each 



*See Chapter VII. 



