256 
H. S. REED 
The Quartile Deviations of Plants Starting in the Several 
quartiles 
The classification into quartiles having been made, it was of interest to 
study the behavior of plants starting in a given quartile. Tables 3 to 6 
show the quartile position, at each observation, of the plants which were 
in a given quartile on the 14th day. The measurements of the plants on the 
7th day were grouped so closely about the mean that the limits of the quar- 
tile range would have been far inside the errors of measurement. The 
average height for the population on the 7th day was 17.93 cm. with a 
standard deviation of only 1.62 cm. ; only 10 plants fell outside of a range of 
16 to 19 cm. 
A brief inspection of table 3 will make clear the method of ascertaining 
the quartile positions of the plants at successive intervals of time. It is 
there shown that there were 15 plants in quartile I on the 14th day. On 
the 2 1st day, 12 of these were still in quartile I, two were in quartile II, 
and one in quartile III. The mean quartile position of these plants on 
the 14th day was obviously i.ooo, on the 21st day it was 1.226. As time 
went on, these 15 plants were gradually more widely distributed through 
the several quartiles, and at the close of the growing period the mean 
quartile position, was 2.266 with the comparatively large standard deviation 
of I. 18. 
A more concrete idea of the distribution may be obtained by reference 
to the figures in the next to the last column of the table. There were 10 
distributions, each containing 15 observations, or a total of 150. From 
the figures in the "total" column, it is seen that 68 observations fell 
in quartile I, 31 in quartile II, 28 in quartile III, and 23 in quartile IV. 
The same values are expressed in percentaegs of the total number of obser- 
vations in the last column. 
The observations on the quartile positions made on the 14th day were 
excluded from the computations, since they were, by hypothesis, in a certain 
quartile on that day, and we could not assume that the laws of simple 
sampling would apply if they were included. 
If we note the total number of observations in the various quartiles, 
it will be seen that the plants which were small on the 14th day tended to 
remain small to the end, half of the total number of observations being 
located in the first quartile and the remainder being scattered through the 
other three quartiles. 
An inspection of table 4 shows the behavior of plants which were in the 
second quartile on the 14th day. Here again it will be seen that plants 
which started in this quartile tended to remain in it. Of the total obser- 
vations, 37 percent were in the second quartile. In comparison with the 
plants which started in the first quartile, there is a somewhat greater ten- 
dency toward dispersion. It might be argued, and with justice, that such a 
tendency might logically be expected, since the plants starting in the first 
