386 MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION 
I find: 
Mean height = 67°2989. 
Standard deviation = 2’°5848. 
Maximum ordinate, 3994:04. 
This gives a very close-fitting normal curve. 
The data for a generalised curve are 
po = 6°68122 B, = 005769 
Po — 1368 B, = 3°024801. 
By = 1385°023824 
Thus, 
2B, — 3B, — 6 = 032295, 
and being positive, we see the curve belongs to Type IV. There is, thus, exactly as in 
the previous examples of crab measurements, no range of a limited character for these 
statistics of height.* For a true normal curve, 6,, 8, ought to be 0 and 8 respec- 
tively ; we have therefore a still closer approach (3°025) than in the case of the crabs 
(8°128) to normality. In this case 7 is about 400, and on any reasonable scale, there 
is no sensible difference between the normal and the generalised curves. The skew- 
ness is very slight, = ‘038 about, or about half its value in the case of the crabs. 
24. Example I1V.—Height of 2192 St. Louis School Girls, aged 8.—The following 
statistics are given by W. T. Porter, “The Growth of St. Louis Children,” ‘ Trans. 
of Acad. of Sci. of St. Louis,’ vol. 6, p. 279, 1894. 




| | 
| Heichts at intervals of | @ i Heights at intervals of | 
| . 2 centims. Number. 8 2 centims. Number. | 
| | 
centims. | centims. | 
| 141 and 142 | 1 119 and 120 342 
| 139 ,, 140 0 4) UWS 321 
| sy? s Je%s} 1 | Ws. HIS 297 
| 135% e136 5 | aL Seen lela | 222 
Some eelod 10 | Wo, le 137 
NS, “Sy 21 109 Re lO 84 
WP) NBO) 28 | 1072 S108 | 42, 
Wey US) 79 | 105. 5, 106 27 
125 126 138 | 103 ,, 104 8 | 
NERS oo pA 183 | OTe 102 2 
Weil 5 ale 248 i 995 100 1 




The following are the calculated values of the constantst :— 
* Tf, notwithstanding, we take a curve of Type III., we find the range limited on the ‘dwarf’ side 
at about °7645". 
+The unit of all these constants = 2 centims., except in the case of the mean height. The 
standard deviation = 5°55244 centims., which gives a probable deviation of 3°745 centims. The mean 
