Importance of Determining Limits of Error. 263 
would more nearly correspond to the total of the first grade, 
one-half million, on the supposition that all pupils were first en¬ 
rolled in the first grade. 
The other chief error, taken by itself, would make our final 
second grade per cent, too large — namely, the fact that our 
percentage 1 (282, 992), is too large. It is too large by approxi¬ 
mately one-third, since about thirty-three per cent, of any 
second grade enrollment appear to be pupils who remain in the 
second grade two years (p. 267, infra). 
The death rate and the fluctuations of population do not mate¬ 
rially vitiate this method, as will be seen later (p. 270). The 
former is never an appreciable quantity, and the latter is inop- 
perative because we are here dealing not with classes as they 
actually advance through the grades, but with the proportionate 
enrollments in the various grades at all times — and we might 
say in all places; for national and even European statistics cor¬ 
respond in a general way to those of Chicago and Milwaukee. 2 
In the latter case, no matter how many families would remove 
to or from Chicago, it would not change the proportions that 
enroll in the various grades. 
The most important correction, therefore, to be made under 
this method, is to eliminate the second enrollment that each 
pupil made in any grade. We could then be sure that we had 
reached the minimum limit in our second grade average; and 
could also compute the average number of grades that each pupil 
had attended. This brings us to one of the main topics of the 
paper. 
IMPORTANCE OF DETERMINING LIMITS OF ERROR. 
Let us stop to remind ourselves of the main aims of the 
paper. The first aim is to determine what per cent, of pupils 
drop out at each grade. This we seem already to have approxi¬ 
mately secured, to judge by the methods discussed later, for 
they only corroborate the results of the deductive method. It 
seems that the errors which tended to make the per cents first 
1 This word is used throughout the paper in the strict sense to designate 
concrete numbers, not the corresponding per cents. 
2 See Enrollment of Various Countries , p. 273. 
