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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§.