ON THE USE OF INDEX NUMBERS. 861 
_ though the figures for one or other period may not be absolutely correct. 
Since each one is liable to the same chances of error, the relative accu- 
- racy may thus be quite sufficient for purposes of comparison. 
The most recent instance of the use of index numbers is perhaps that 
contained in this year’s report upon ‘Changes in Imports and Exports,’ 
rendered by Mr. Robert Giffen to the Secretary for the Board of Trade. 
The object here sought for is to ascertain the yearly progress of the 
nation’s trade with colonies and countries outside its own borders, both 
as regards its money value and the volume of the goods which it receives 
and parts with. This, so far as the value is concerned, is easily ascer- 
tained by the figures published year by year in the ‘ Statistical Abstract,” 
which sets forth the value of each principal article of both import and 
export, with the combined value of all the minor articles, and then 
collects them all into one total which shows in one sum the aggregate 
import, and in another, that of export. Thus we find without any calcu- 
lation that in 1883, the last year with which the paper deals, the imports 
were yalued at 427,000,000/., whereas ten years ago they were at 
371,000,0001., showing an increase of 56,000,0007. Also that the values 
of the exports at the same dates were 240,000,0007. and 255,000,0001., 
the difference being 15,000,000/. against the later period. In like manner 
that the sum total at one time was 667,000,000/., and at the other 
626,000,000. Also that the imports exceeded the exports in 1883 by 
187,000,0001., and in 1873 by 116,000,0007. These particulars are by 
no means all that are needed for the formation of a true judgment as to 
our trading prosperity or adversity. To the banker or the broker it may 
be sufficient to know the gross amount on which commissions may have 
been earned or charges realised; but the merchant needs to understand 
the changes in the goods which have passed through his hands, the 
shipowner has to take note of the quantity of goods he has carried. So. 
the economist looks to be informed of the volume of our trade, and 
it is the business of the statistician to evolve from such data as are 
within his reach the fullest information they are capable of furnishing. 
This is not so easy as at first sight it appears to be. 
The ‘Statistical Abstract,’ the only source of information dealt with 
on the present occasion, sets forth the principal articles in quantity where 
that is capable of expression, and the respective values for each enume- 
rated article, all others being included in one total of value only. If the 
investigation be confined to one article alone, little more than inspec- 
tion is needed. Take for instance pig iron, of which we exported in 
1883, 1,564,000 tons, at a value of 4,077,0001., and in 1873, 1,142,000 
tons, at 7,118,0001.; and cotton yarn 265,000,000 lbs., at 13,500,0002. in 
the one year, and 215,000,000 lbs., at 15,895,000/. in the other. There 
is no difficulty in seeing wherein the quantities and values have in each 
case changed, but inasmuch as the quantity of one is stated in tons 
and the other in pounds weight, and the unit values are in pounds and in 
pence, we cannot as with the money add the two together, to see whether 
on the whole the bulk has increased and in what proportion. Much less 
could all the goods having the quantities in yards, gallons, &c., be thus 
brought into one representative sum. Mr. Giffen therefore takes 100 as 
the index number for the total value, say of exports in 1883, which we 
have seen to be 240,000,0007. Then to find the proportion of the pig 
iron value, says, as 240,000,000 : 4,077,000::100:1°7, the index 
number for pig iron; and as 240,000,000 : 13,500,000 ::100 : 5°6, the 
