The nature of capital and income

Bibliographic data

Monograph

Identifikator:: 102659555X

URN:: urn:nbn:de:zbw-retromon-82920

Document type:: Monograph

Author:: Fisher, Irving http://d-nb.info/gnd/118533541

Title:: The nature of capital and income

Place of publication:: New York

Publisher:: The Macmillan Company

Year of publication:: 1923

Scope:: XXI, 427 Seiten

Digitisation:: 2019

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

id ® 408 NATURE OF CAPITAL AND INCOME The “standard deviation” plays an important role in the treatment of all statistics involving variation about a mean. One of its simplest uses is to change any given deviation into a deviation relative to the standard deviation (or to a fixed portion of it). This is usually done by dividing the absolute deviation by the standard deviation. Thus, in the above ex- ample, where the standard deviation is.95 9, an absolute devia- tion of, say, 29, mean is a relative deviation of 2 + .95 or about 2.1. : Such a reduction from absolute to relative deviation brings the different probability distributions or curves into a common comparison, so that probability tables may be constructed applicable to all. In one case the deviations may mean inches of rainfall, in another, pounds of barometric pressure, in an- other, the annual percentage of dividends, as in the case above. These are incommeasurable. But if each be compared with the standard deviation which applies to that particular case, and which would therefore be measured in inches, pounds, or annual percentages, respectively, we obtain three ratios which are simply pure numbers indicating the extent of the deviation compared with the standard deviation. If we now consult a probability table we may find at once what is the probability of any given relative deviation. For the chance that dividends will, in the case supposed, deviate in any given future year by 29 from the mean rate of 4.99, is, from the tables, 1 in 20; for the deviation, measured relatively, is, we saw, the number 2.1 and the probability cor- responding to this in the tables’ is 18. This expresses the chance that the deviation will keep inside the limits of 29; i.e. that the dividends will be between 2.99, and 6.99%. The wider the range of deviation considered, the less the chance that the actual dividends in any year will fall out- side that range. Moreover, the chance decreases far faster than the range increases. This relation, which follows from the theory of probability, has very important consequences in 1 Thus on p. 66 of Davenport’s ‘Statistical Methods,” New York, Wiley, 1899, we find for a relative deviation 2.1, the number .4822 as the chance of the deviation in one direction. Hence the chance of the devia- tion in either direction is double this or .9644, about 1§.

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