DIAGRAM 2.- Per cent of the population enrolled in the common schools. m 194 1870-71.. 19.11 1886-87.. 20.2 20.35 20, 96 a Subject to correction. TABLE 7.-The average daily attendance at various periods, and its relation in 1901–2 to the enrollment. 8, 153, 635 | 10, 632, 772 10, 999, 273 613, 275 73. 42 63. 43 66. 46 69.91 68. 91 North Atlantic Division. Maine. Pennsylvania Delaware Florida Kentucky. Indian Territory s. Ohio Kansas. Montana.. . Approximately. Method of ascertaining arerage attendance. The average daily attendance during a year (which is the average number of pupils actually present each day the schools were in session) may be computed as follows: First, for a single school: Add together the number of pupils present each schowl day during the year, and divide the sum (which is the “aggregate attendance in days?') by the number of such school days. Second, for a group of schools having the same number of school days in the year (as the schools of most cities have): Divide the combined aggregate attendance in days of all the schools by the number of school days in the year. Third, for a system of schools having different lengths of school year (as, for instance, those of a county): Add together the average attendance of the component schools and groups of the system, as ascertained by the foregoing rule. For larger systems, as those of a State or of the United States, the summing-up process is continued in the same way. In a system of schools such as is specified under the heading “Third," the average number of days in the school year for the whole system is found by dividing the combined aggregate attendance in days of all the schools of the system by the arerage attendance as ascertained by the method given. See observations on Table 8. Observations on ascertaining the arerage school term (Table 8).—The “aggregate number of days' schooling given" to all pupils (see column 7), which is the same thing as the aggregate number of days attended by all the pupils, has been computed for those States which do not make an explicit report of this item by multiplying the average daily attendance of pupils by the average length of school term in days. Conversely, the average length of school term (column 6) for the United States as a whole and for each of its geographical divisions has been obtained by dividing the aggregate number of days attended by the average daily attendance. By this method the school term of each State, in computing the average term for a number of States, is in fact given a weight proportioned to the school attendance of the State, as should be done under a correct interpretation of the expression, "Average length of school term.” The result might more properly be called "Average length of attendance,” which is essentially what it is desired to know. A method which has been in use in some States for finding the average school term of a county, for instance, is to weight the different school terms of the towns or districts the county is composed of by the number of schools in each. In other words, the total number of days (or months) all the schools of a county were kept is divided by the total number of schools to get the average time each one was kept. So, in finding the average term for the State, the school is taken as the unit instead of the pupil. When the schools differ much in size (number of pupils), as they do in all mixed urban and rural systems, varying from some half a dozen to 500 or more pupils each, the average term obtained by this method varies considerably from that obtained by the Bureau's method. The long terms of the large city schools not being given their proper weight, the resulting average is too small. The same objection applies still more forcibly to weighting the school terms of the different counties or towns by the number of school districts in each. Another method is to divide the total number of months or days taught by the number of teachers. This is better than the preceding method, as it takes some account of the size of the schools--that is, an eight-grade school with eight teachers has eight times the weight, in determining the average term, that a district school with one teacher has. This is manifestly as it should be. If every teacher taught the same number of pupils the result would be the same as by the Bureau's method. Care must be taken in working by this method to use the number of teachers' places (or number of teachers necessary to supply the schools) for the divisor; for if a teacher teaches a school or grade part of the term, and is replaced by another for the rest of the term, the two should obviously count as one teacher for the combined period of service. The liability to overlook this distinction in practice, as well as the inequality in the number of pupils to a teacher, makes this method generally objectionable. Still another and most faulty method is to add together the school terms of the different counties or towns and divide by the number of such counties or towns; i. e., the simple arithmetical mean is taken. An example of this occurs in a school report, where it is stated that 14,193 pupils in one district attended 185 days and 856 pupils in another district attended 160 days, while the average time the whole 15,019 pupils attended is computed at 172 days, although nearly all (16 out of every 17) attended 185 days. This method, if it can be so called, gives altogether too short an average term, and nothing can be said in defense of it. It is as if, wishing to get the population per square mile of Minnesota and Dakota combined, we said, population per square mile of Minnesota, 9.86; of Dakota, 0.92; average number of persons per square mile in the combine territory (0.92 +9.86)2=5.39, instead of dividing the total population of the two States by the combined area in square miles. The "aggregate number of days' attendance” is a statistical item of the utmost simplicity and of great value, about the meaning of which there can be little or no difference of opinion. Every teacher's register that records the number of pupils present each day in school, as they all presumably do, contains the data for ascertaining it for that school for the school year by the simple process of addition or summing up. There are a few States that do not ascertain at all how long their schools were taught, and others that use methods so faulty that they also are totally in the dark in the matter. Yet this is one of the most necessary and fundamental items of information in determining the amount of school instruction given. TABLE 8.—(1) Average length of school term at various periods; (2) aggregate number of days' schooling given to all pupils; (3) the same compared with the school population and the enrollment (columns 8 and 9). 132.1 130.3 134.7 114.3 145.0 1,594, 738, 835 152.0 159. 2 92. 4 79.2 139.8 129.2 166.6 99.9 88.2 148.0 135.0 177.5 112.1 99.8 155.9 141.5 177.3 115.8 100.6 156.5 143.9 98 70 115.6 169 170 172.4 176 178 127.2 109 105.3 125.5 177 184 179 178.5 192 133.4 112 117.7 136 177 188 182.5 186.5 141 147 147.65 140.05 156, 15 154 189 6185 191 192 189.01 188.89 175 177 186 186 166.6 166.4 192 147.6 158 187 193 112.8 €170.1 1190 176 6122 132 76.8 59 118 86.9 87.3 d113 94 50 70 d 65 94 86 United States. Maine... Pennsylvania Delaware Florida Kentucky Indian Territory Ohio Kansas. 1110 66.5 102 68 81.3 73.5 74.5 d 86 78.8 100.6 71.7 100 d 75 71.6 100.1 485, 954, 340 91.2 130. 2 73. 4 66.9 109.4 14, 540, 946 9,819, 420 89.6 93. 8 92.7 101.8 93.5 84.9 83.7 108. 9 102.6 116.6 0 146.6 141.6 138.0 133. 2 125.2 124.7 (87.9 b 76.6 106.3 b46.3 59.4 35. 9 38.0 47.4 45.9 €116.6 6114.9 139, 1 6 72. 2 76.1 50.3 66.8 70.9 70.9 Montana 117.5 104.3 48.1 38.4 141.4 35.9 50.0 43.1 48,5 13.8 66.0 b 63.0 67.4 6 57.4 84.6 74.9 57.7 59.9 97.2 165 152 152 163.8 1 160 169 160 144 155.7 9129.1 135 126. 25 165 153.9 cd4, 303, 530 6,687, 296 17, 956,532 18, 188, 319 7,965, 291 32, 930, 655 b31, 442, 463 24, 600,000 16,829, 040 2, 150, 634 61, 769, 388 127, 764,519 b 54, 432, 300 6 47,119,014 40,671, 922 59,856, 480 67,879, 124 7, 202, 641 2,321, 690 780, 178 89.9 88.3 94.5 0 82.3 6 75.5 74.5 94.1 72.0 64.7 72.8 93.7 77.8 121.1 110. 3 131.5 6 106.7 b 105.6 98.1 106.9 96.5 86.1 91, 2 105,5 88.3 d 89 d 200 92 (111 0 152 142 45 d 80 d90 123 107 119.8. c107 85 054.1 od 48.1 74.0 34.5 39.9 89.7 85,2 72.1 68.0 94.2 99.7 874.3 od 73.3 85.6 57.8 74.9 112.1 112.2 80.9 77.7 104.8 125.9 a (ertain States report their school term in months: these months have been reduced to days by multiplying by 20 in each case. bIn 1900-1901. d Approximately. In 1893-94. |