298 Trans. Acad. Sci. of St. Louis. 
either may be used for the type without any error of prac- 
tical importance, provided the series are similar to those 
analyzed here. This point is of practical interest because 
the labor of reckoning the average is much greater than in 
reckoning the median value. 
Bowditch, in The Growth of Children, Boston, 1891, p. 
495 et seq., discusses the relation of median and average value. 
‘‘{t is evident,’’-he writes, ‘‘ that the value M will tend to 
‘* approximate to the average value of all the observations and 
‘* will be identical with it when the [percentile] curve S T 
‘‘is symmetrically disposed on both sides of M, 7. e., when 
‘‘the values at sixty, seventy, eighty, ninety and ninety-five 
‘*per cent. exceed M by the same amount, respectively, by 
*‘which the values at forty, thirty, twenty, ten and five per 
‘cent. fall short of it. If A represent the average value of 
** all the observations, then the value of M—A will be a meas- 
*‘ure of the direction and extent of the asymmetry of the 
‘ccurve S T, for this value will be zero when the curve is sym- 
**metrical, positive when the values at the lower percentile 
** grades fall short of M more than those at the higher grades 
‘‘exceed it, and negative when the reverse is the case.’’? [Dr. 
Bowditch now gives a table of median minus average height 
and weight.] ‘An examination of this table or of the curves 
‘constructed from it, as given in Plate I, shows that the 
‘asymmetry of the curves of percentile grades varies very 
**much, at different ages, both in direction and amount. The 
** variation in the value of M—A in the curves of height is much 
**the same as that in the curves of weight for each sex consid- 
‘‘ered by itself, but there is a great difference between the 
**two sexes. This difference shows itself most distinctly 
“*between the ages of eleven and fifteen years. During this 
**time a rise in the curves for the males coincides with a fall 
‘in those for the females, while before and after this period 
‘the curves, as a rule, rise and fall together. We must con- 
“clude, therefore, that the rate of annual increase, both in 
‘height and weight, is different at different percentile grades, 
** or, in other words, that large children grow differently from 
**small ones, and moreover, that between the ages of eleven 
_ ‘Sand fifteen years there is a striking difference in the mode 
“Sof growth of the two sexes.’’ 
