168 Trans. Acad. Sci. of St. Louis. 
When these tables are examined it is seen that in each age 
the mean weight of pupils in the higher grades is greater 
than the mean weight of all pupils at that age and exceeds 
still more the mean weight of pupils in the lower grades.* 
This fact is more conspicuous when the grade weights in 
Tables No. 2 and No. 3 are expressed graphically. The curves 
thus secured are reproduced in Plate I. The mean weight of 
all pupils at each age is marked onthe curve by a small 
perpendicular line near the figure indicating the age. The 
abnormal deviation of the ends of some of the curves from 
the general slope of the curve is due to the number of obser- 
vations at these points being too small for trustworthy 
results. 
The truth which the curves in Plate I express is very plain. 
They declare in unmistakable lines that precocious children 
are heavier and dull children lighter than the mean child of the 
same age. They establish a physical basis of precocity and 
dullness. 
Whether means or averages are the more trustworthy tools 
in investigations of this sort is a matter of opinion. So long 
as their respective value is a subject of controversy investi- 
gators will accept no results as final which can be supported 
only by means. It must therefore be my first concern to 
show that the law: MEAN PRECOCITY IS RELATED TO MEAN PHY- 
SICAL DEVELOPMENT may with equal truth be written: 
AVERAGE PRECOCITY IS RELATED TO AVERAGE PHYSICAL DE- 
VELOPMENT. 
In Table No. 5 are found the average weights of boys dis- 
tributed by school grades, and the average weights irre- 
spective of grade. Pounds are in DOUBLE-FACED type and 
kilograms in ‘* lower case’’ type. The number of observa 
tions is in each case the same as in Table No. 2. 
* The end weights of the series at same age are calculated from so small 
a number of observations that they sometimes vary from the law which the 
more numerous observations toward the middle of the series show to be 
true. 
