The purpose of combinations of this nature is to take cognizance of the general trend of affairs. In times of increasing prices which the United States has just experienced an increase in the value of sales would be normal. , A careful analysis by various other factors, price quantities and the like would be neces sary to determine whether the business was going back, holding its own or increasing.
Let us suppose that we have before us the ber sales of the year 1920. Are they large or small? Comparison with 1919 may show an advance. If this advance is greater than the price advance of 1920 over the previous year, the question, of course, is an swered. If, however, the gross sales for the first nine months of 1920 show a very marked increase over those of the corresponding period of 1919, the Sep tember sales might well be higher than those of the same month a year before, and yet mark the begin ning of a downward movement. Not one but many comparisons may be needed to bring out the full sig nificance of the facts.
19. The percentage.—One of the most frequent de vices for making figures comparable is the reduction to percentages. This is essential when the units com pared are of different sizes. That one concern has an advertising expense of $50,000, and another one of $120,000 per year, tells us nothing unless we know the volume of sales to which these figures relate. With these facts we have the ratio of expense in each case. But it is difficult to compare two ratios with one an other unless they have some common term. If in each case the advertising expense is expressed as a per centage of the total expense, the ratios are comparable.
In discussing a series of percentages care should be taken not to express the difference between the num bers of the series as so much per cent unless this is strictly what is meant. If the series of percentages compared is A, 78; B, 82; and C, 96; we not infre quently hear it stated that B is 4 per cent higher than A, while C is 18 per cent higher than A. This is not the fact, as these differences are points, not percent ages. To express them in percentages A must be taken as the base, and it will be found that B is 5.1 per cent above A, while C is 23.1 per cent above A.
When a percentage has been calculated for the numbers of a series, as the months of a year, or a quarter, and the average percentage for the whole period is then wanted, the mistake is sometimes made of cakulating this average from the individual per centages and not from the totals of the original fig ures. The following supposed case will illustrate.
The percentage given for the quarter is the cor rect one based upon the division of the total selling ex penses by the total sales. Had the percentages for the three months been added and the total divided by three, the result would have been 11.9.
20. The ratio.—The ratio between one fact and another is of frequent use in official and business sta tistics. Instances are shown in the per capita con sumption of wheat, sugars and other commodities; in railway receipts per mile of road, in costs per unit of product and in many others. Here again the cau tion should be given that such comparisons may tell as much about one factor as. another. Comparison of per capita sales of farm implements in Rhode Island and North Dakota for example, would not indicate much about the character of farming in these two re gions, but chiefly that one was a farming country and the other was not. Sometimes such ambiguity can be avoided by a better choice of things compared. Consumption of fertilizers for example would be com pared more appropriately with the acres of improved land in farms in the different states than with the number of the population.
21. Graphic statements.—It is a variation of the usual statistical form of the statement when the facts to be expressed are not given in figures, but are shown in pictorial form, by means of lines, curves, surfaces and other geometric figures. Such graphic methods are coming to play a larger and larger part in the business world. Executives, sales managers, and ad vertising men are finding a constantly increasing use for such methods of presentation as a means of grasp ing rapidly the results of business administration which are vital to the work in which they are engaged.
The use of charts and diagrams, or to borrow the term which the scientists have introduced into the lan guage and which is making its appearance in general writings, of "graphs," owes its growing frequency to the apparent ease with which such representation of facts can be understood. There are many persons to whom series of figures carry no significant message, but who can readily see the proportions of things, their increase and decrease, and the other relations which are expressed by statistics, when they are shown in the form of the diagram or chart. It may well be that this applies to the majority of persons, and that only those trained in the use of figures can grasp their real significance. This, however, is a training which comes with practice, and because of the limitation of the graphic methods, is not to be overlooked.