FIG. 19.-Distribution of 80 cities according to the percentage of pupils over age in each grade, 1917-18.

at 28-31; and in the sixth grade at 32-35. Beyond this grade the mode recedes, falling at 16-19 in the seventh grade and at 12-15 in the eighth grade. In the high school the mode is located in the 16-19 group for both the first and second years, and in the 8-11 group for the third and fourth years. The "procession" of modes in this diagram is more or less analogous to the "over-age" curve shown in figure 16. The apex of the curve in figure 16 falls in the fifth grade, while in figure 19 the sixth grade had the mode of greatest magnitude. This modal practice characteristic of the sixth grade implies that the largest group of cities hold their pupils through the sixth grade regardless of the proportion of over-age children. In figure 30 it is shown that more children are found in the sixth grade than began five years before.

TABLE 20-Frequency of the ratios between the number of boys and of girls found in the first grade and the number of boys and of girls in the largest age group in 80 cities in 1908 and 1918.

It is important to know how many children survive to the different grades. To ascertain exact data for each of the 80 cities for the two dates 1908 and 1918 would have been an onerous task. No single number can accurately represent the number of beginning children in 12 successive classes. Approximate results, however, can be obtained by dividing the total enrollment in each grade by the largest age group. This is a convenient means of ascertaining fairly comparable percentages for the different cities, although it is generally understood that the divisor chosen is too large for most of the

grade groups, especially for the high-school grades. To have used an average of the largest age groups would have distributed the inaccuracies over a wider range, reducing the major errors in the upper grades, but increasing minor errors in the lower grades.

10

15

20

BOYS FIRST GRADE.

20

20

6

FIG. 20.-Distribution of 80 cities according to the ratio between the total enrollment and the largest age group in the first grade in 1908 and 1918.

In figure 20 the percentage relationship between the largest age group and the enrollment in the first grade usually exceds 100. If this ratio is found to be 150, it means that there are 50 per cent more children in the first grade than actually begin. In other words one

third of the children in this grade would be "repeaters." In a few cities this ratio exceeds 200 indicating that half the pupils in this grade are "repeaters." For boys in 1908 the modal ratio on this score was 130-139, but in 1918 it had increased to 140-149. For girls the modal ratio in 1918 fell in the group 120-129. For 1908 the corresponding ratio was not well defined but probably was best typified by the percentage group 140-149. On the whole the black curves in figure 20 fall to the left of the respective dotted curves, indicating a slight reduction in the percentages of pupils repeating the first-grade work. The change, however, is not marked, showing that school systems have not completely solved the first-grade accumulation problem.

TABLE 21.-Frequency of the ratios between the number of boys and of girls found in the second grade and the number of boys and of girls in the largest age group in 80 cities in 1908 and 1918.

TABLE 22.-Frequency of the ratios between the number of boys and of girls found in the third grade and the number of boys and of girls in the largest age group in 80 cities in

TABLE 23.-Frequency of the ratios between the number of boys and of girls found in the fourth grade and the number of boys and of girls in the largest age group in 80 cities in

1908 and 1918.

1908 1918 1908 1918 1908 1918 1908 1918 1908 1918 1908 1918

In the second, third, and fourth grades the curves for 1918 fall to the left of those for 1908, indicating a general reduction in the percentage of repeating pupils in these grades. This condition does not