APPENDIX IIL 
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 economie 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, ¢.g., supplies of wheat from year to 
year, area in wheat, imports, exports, ete. 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. 
