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The method of procedure was the following. Observations are available from the following six cities: Boston, Milwaukee, St. Louis, Worcester, Toronto, Oakland. These represent a variety of conditions. We may assume that the variations represented by various cities are due to accidental causes, that is to say, that when the children in all the towns and cities of the country are measured we expect to find the results to vary around a certain average, according to the laws of probability. The type of the total population would embrace statistics of all the individuals of various ages. These are not available, and we must consider the cities in which the measurements were taken as representatives of the total population. In order to unite the material properly we ought to know how large a portion of the population is represented by each city. We can not obtain any satisfactory information on this point, and the only practicable way of uniting the material seems to be to add all the measured individuals, without regard to the varying numbers that were measured in each city. This has been done. It was necessary to reduce the observations that were recorded in inches to centimeters. Similar reductions were necessary in the tables of weights. This required a lengthy interpolation. The St. Louis measurements required an additional interpolation, as the age of the measured children was recorded at the nearest birthday, while all the other observers counted age from the last birthday. The results of this calculation are given on pages 1555 and 1556.

It will be noticed that the distribution is rather unexpectedly irregular. I presume this is due to the fact that observers developed a tendency to round their observations, so that full inches and the centimeters ending with 0 or 5 (110, 115, 120, etc.) were given undue preference. It is likely that if this fact had been considered, the resulting curves would have been smoother.

Frequencies of statures of American boys, in percentages.

centimeters.

Height in

Ages, in years.

5.589 6.536 7.511 8.504 9.496 10.494 11.492 12.489 13.481 14.487 15.454 16.445 17.453 18.424

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Cases

1,535 3,975 5,379 5,633 5,531 5, 151 4,759 4,205 3,573 2,518 1,481 753 429

2:29

Average

height... 106. 41 111.78 116. 89 122, 06 126.89 131.75 136. 17 140. 68 145. 88 152. 14 159. 48 164. 68 168. 81 170.91 Average

variation +3.83 Mean vari

ation Corrected

average

for half

year Mean vari

ation cor

rected Mean vari

ation at

+4.81

+3.98 ± 4.17 +4.35-4.56 ±4.78 ±4.97 +5.35 ±6.04 ± 6.88 ± 7.31 ±6. 155.78 ± 5.45

±4.92 +5.22 +5.53 £5.66 ±5.90 +6.32 ± 6.79 ±7.69 ±8.65 8.92 ± 7.77 +7.25 +6.76

105.90 111.58 116.83 1:22. 04 126. 91 131. 78 136. 20 140.74 146. 00 152.39 159. 72 164. 90 168.91 171.07

+4.80 +4.92 ±5.22 +5.53 +5.66 ±5.90 +6.32 ±6. 80 +7.71 ±8.66 ±8.87±7.75 £7.23 ±6.74

half year±(4.40) ±4.66 ±5.00 +5.34 ±5.48 +5.74 +6.20 +6.62 +7.54±8.49 ±8.6117.63 4.7. 15

Frequencies of statures of American girls, in percentages.

Height in centi

meters.

Ages, in years.

5.611 6.545 7.513 8.501 9.497 10. 495 11. 494 12. 490 13. 479 14. 471 15. 466 16. 473 17. 466

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1,260 3,618 4,913 5, 289 5, 132 4,827 4,507 4, 187 3, 411

2,537 1,656 1,171

790

Average height 105. 45 110.32 116.16 121. 21 126. 13 131. 24 136. 58 142. 46 148. 58 153. 41 156. 45 158. 00 159, 11
Average variation. +3.74 +3.98 +4.23 +4.45 +4.51 ±4.91 ±5.45 ±5.98 ±5.89 ±5. 18 +4.68 ±4.64 ±4.43
Mean variation. +4.69±5.09 +5.25 +5.58 ± 5.73 ±6. 18 +6.83 +7.57 ±7.38 +6.71 ±5.96 ±5. 79 +5.75
Corrected average 101. 88 110.08 116. 08 121.21 126. 14 131. 27 136. 62 142. 52 148. 69 153. 50 156. 50 158.03 159.14
Mean variation
+4.64±5.07 +5.25 +5.58 ±5.73 ±6.18 ±6.83 ±7.57 ± 7.37 ±6.69 ±5.96 ±5.79 ±5.75

corrected

Mean variation at half year

+4.78 +5.01 +5. 46 +5.54 ±6.00 ±6.63 +7.41 £7.20 +6.57 ±5.88 +5.65

From the preceding facts and considerations we conclude that the averages and variabilities of growing children must not be considered more than indices of the typical conditions characteristic of a certain age. In order to determine these accurately, the asymmetry of the distributions must be taken into account. This, however, can not be done, except by the expenditure of a vast amount of labor, until a sufficient series of observations, taken according to the individualizing method, is available.

GROWTH AS DETERMINED BY THE TOTAL SERIES OF TORONTO CHILDREN.

I give first of all a table of statures grouped in periods of quarter years. In this tabulation all those individuals who did not expressly state that their age was so

and so many years and no months were omitted, because there is a considerable probability that in many cases of this sort the number of months was not recorded. For this reason the number of children corresponding to the full years and no months is too small. It might have been better to group the material as follows: 11, 0, 1 months; 2, 3, 4 months; 5, 6, 7 months; 8, 9, 10 months; but I did not do so, in order to preserve the comparability with other series which extend over the whole year. The records of ages show that in order to obtain accurate results the question ought not to be simply for years and months, but we should ask for the age at the last birthday, age at the coming birthday, and the date of the birthday. When we simply ask for years and months, the person answering the question will often first give the age at the nearest birthday, particularly when the approaching birthday is not far distant, and then add the number of months passed since the last birthday, thus introducing an error of a whole year. This was noticed to occur in the Worcester measurements that were repeated after the lapse of a year, Accuracy can be attained only by the three questions given before.

The following are the tables of statures:

Statures of Toronto boys, grouped in quarter-year periods.

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103.9 104.5 107.3 108.1 109.7 110.3 111.1 113.1 114.9 115.5 117.7 118.3

+4.444.70 ±5.07 ±4.60 +4.59 +4.48 +4.29 +5.25 +4.17 ±4.67 ±4.83 +5.40

Statures of Toronto boys, grouped in quarter-year perioas-Continued.

Number of boys of the following ages.

Height in centimeters.

8 years and

9 years and

10 years and

0 to 2 3 to 5 6 to 8 9 to 11 0 to 2 3 to 5 6 to 8 9 to 11 0 to 2 3 to 5 6 to 8 9 to 11

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Cases.

198

Average height

251 260 229
119.7 121.3 122.2 123.5 125.1 125.6 127.0 127.9 129.9 130.2 132.2

194 241 242

228

167

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990

132.9

Mean variation.

15.08 16.01 +5.31 15.13 14.47 £5.43 +5.51 +5.99 +6.00 +5.97 +6.01

+6.09

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