THE STATISTICAL STUDY OF VARIATION 43 
by the corresponding frequency (f.d’); divide the difference between the 
minus and plus products by n to obtain correction factor (w); then 
multiply each f.d’ by d’ to get f.d’; summate the last. products and 
divide by n; from the quotient subtract w? and then extract the square 
root. The illustration, Table VI, is based upon the same data as the 
preceding. 
The short method of computing the standard deviation is the 
more accurate because of the elimination of many decimal places. In 
addition to the complete short method there is shown in the last 
column on the right a very useful method of checking the computa- 
tion. Each f(d’ + 1)? is calculated algebraically. Thus in the first 
case f = 3 and d’ = —3;-substituting we have 3(—3 + 1)? = 12. In 
the same way X(f) + 25(f.d’) + 3(f.d’) is computed algebraically. 
Substituting we have 400 + (—34) + 701 = 1067. 
The standard deviation, being a measure of absolute variation, is 
exceedingly useful in comparing the variability of one variety with 
another with respect to the same character, or of the same variety in 
different years with respect to a given character, or of one character with 
another in the same or different species. For example, Love and Leighty 
in their memoir on ‘Variation and Correlation of Oats” give the means 
and standard deviations for total yield of plant in grams (as well as for 
eight other characters) for the same pure strain of Sixty Day oats for 
three years as follows: 
1909 — M = 4.032, o = 2.249 
1910 — M = 3.458, o = 1.323 
1912 — M = 7.962, o = 3.353. 
The differences between these values are due mainly to differences in 
climatic conditions during the three years, the year 1910 having been 
especially dry and hot. Similar differences appear in the means and 
standard deviations for height of plant, number of culms and number of 
grains produced. This particular observation leads to no new con- 
clusion as it is well known that climatic conditions profoundly influence 
crop yield, but it illustrates the significance of the standard deviation 
as a measure of variation. Furthermore it is of interest to note that 
drouth not only reduces plant growth and yield in this variety but the 
amount of variation as well. 
In 1910 the amount of absolute variation was only one-third that of 
1912. However, the amount of relative variation was not so much 
affected by drouth as might at first appear. When comparing standard 
deviations of different varieties or of the same variety under diverse 
conditions, it should be remembered that the means of the groups under 
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