In curves representing a series of observations, it is advisable, whenever possible, to indicate clearly on the diagram all the points representing the separate observa tions.
The horizontal scale for curves should usually read from left to right and the vertical scale from bottom to top.
Figures for the scales of a diagram should be placed at the left and at the bottom or along the respective axes.
It is often desirable to include in the diagram the numeri cal data or formula represented.
If numerical data are not included in the diagram it is desirable to give the data in tabular form accompanying the diagram.
All lettering and all figures on a diagram should be placed so as to be easily read from the base as the bottom, or from the right-band edge of the diagram as the bottom.
The title of a diagram should be made as clear and com plete as possible. Subtitles or descriptions should be added if necessary to insure clearness.
Ratios and Averages.—In presenting sta tistical information to the public it is gener ally necessary to publish the detailed tables showing the results of the original compilation. Such tables show the numerical relation of totals to totals in one category of data, or of a part or parts to a total, or a part to a part, or of a number of one category to a number of another category. Ratios may be expressed by common fractions, decimals, percentages, or rates per 1,000 or per 100000, etc. Percentages are most commonly used but death and birth rates are usually expressed by the number per 1,000 of general population; and death rates from single diseases, by the number per 100,000. A common form of ratio in business and eco nomic statistics is the number per capita, as money in circulation per capita, as wealth per capita, etc. Crop yield may be expressed as bushels per acre or tons per acre. Density of population is indicated by number of persons per square mile. The ratio to be used in any case is determined partly by custom and partly by the demands of clarity and conciseness of expression.
Averages form another indispensable aid to the statistician in the summarization of data. An average is a quantity which serves to char acterize a number of divergent quantities. The purpose of averages is to express by a single item the net result of a series of items. The cipal forms of averages used in statistics are the simple arithmetic mean, the weighted arith metical mean, the geometric mean, the median and the mode. The simple arithmetic mean is
most widely used. It is computed by dividing the sum of a series of numbers by their num ber. The weighted arithmetic mean is found by multiplying the numbers of a series by co efficients or weights of different sizes and dividing the sum of the products resulting by the sum of all the coefficients. The weighted average is used in cases where it is desirable to give greater emphasis to some items than to others. The geometric mean of a series of n items is the nth root of the product of the items. The use of the geometric mean in sta tistics is limited. Its principal value has been found in the computation of index numbers. The median is that value which "has the central position in a series of items arranged accord ing to size." (Czuber). It an odd number of items is arranged according to size, the median is the middle number of the series. If the number of items constituting the series is even. the median lies between the two central items. The median is less dependent upon extreme values than the arithmetic mean and may often be taken as typical of the series. The mode in a series of items is the value occurring most frequently and around which the other items are distributed most densely. As an average it is more typical than either the arithmetic mean or the median. The mode and median, however, can be computed only for a series of quantitative individual observations such as se ries of wages, incomes, etc.
Index Index numbers are used principally to indicate changes in prices or wages from one period to another. The prices of a certain period are arbitrarily taken as a standard and the index number of such pe riod is fixed at 100. The prices in succeeding periods are computed as p percentage of those of the standard period, a general rise being indicated by an index number above 100 and a general decline by a number below 100. It is obvious that index numbers are valuable only for comparative purposes and that of themselves they give no indication of the val ues from which they are derived. The wide range of possibilities in the selection of com modities, prices and weights and in methods of computation has necessitated standardization of procedure which has been improved from time to time in recent years.