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low or high as compared with the group as a whole. The more accurate method consists in computing the differences between the percentages of the various classes of expenses for the city and the corresponding medians and arranging the excesses and deficiencies in separate lists. As those items that vary most from the medians are of greatest importance, and as variation from the median to the extent of the limits of the middle 50 per cent may be regarded as normal, the computation of differences in cases wherein the city's percentage is within the limits of the middle 50 per cent may be for all practical purposes neglected. The following table presents the result of such a computation for the city of Washington:

TABLE 2.-Differences between the various percentages that lie outside the middle 50 per cents, and the median percentages for the same items, for Washington, D. C

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FIG. 1.-Differences between the various percentages of total expenses that lie outside the limits of the middle 50 per cent, and the median percentages for the same items, for Washington, D. C., based on Table 2.

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Having arranged the facts in tabular form and illustrated them by a diagram similar to the above, the next step in a rational consideration of such facts is to determine in which cases such differences from the normal percentages are justifiable. For, as has been said, peculiar conditions in many cases may either justify large percentages or require the keeping of expenses within low amounts. In order that this process may be more clearly understood, a possible explanation of the variations in the case of Washington is here presented.

Let us start with the percentage in Table 2, that shows the largest deficiency—salaries of elementary school teachers. It has been said above that a high percentage for salaries of teachers would be justified if the average cost per pupil were near the normal. It is likewise true that a low percentage for salaries of teachers could not be considered as contrary to the best interests of the schools if the average costs for salaries were not below the normal. The average costs for elementary teachers in Washington is $21.24 or 88 cents above the median, as shown in Table 29. The deficiency in percentage may not, therefore, be considered as unreasonable or contrary to the best interests of the schools. Such contrast of a relatively low percentage on the one hand and of a relatively high average cost on the other presents an interesting situation. Unusually large amounts must have been spent for other purposes than salaries of elementary teachers in order to make so high an average cost appear so small in the percentage tables or else the number of pupils per teacher must have been unusually small. As the attendance statistics show the number of pupils per teacher to be only slightly below the normal, it follows that certain other expenses must be unusually high. The excess side of Table 2 seems to bear out this conclusion.

Let us now turn to those items in which excesses appear in order to see whether they may be justified. Table 51 shows that the average cost per pupil for salaries of teachers in secondary schools lies next to the median cost. Table 31 shows that the enrollment in secondary schools is larger than that of any city in the group except Chicago. It would seem, therefore, as though the large percentage for this purpose was entirely justified. A larger percentage for supervision of elementary and secondary schools is unavoidable in Washington because of the duplication of positions and salaries in the schools for white and colored pupils. The school buildings of Washington are for the most part small buildings-the eight-room building being the most frequent. This naturally increases the cost of operation and maintenance. It would seem, however, since repairs and fuel for elementary school buildings cost more proportionately than in any other city, and since repairs of secondary school buildings cost more than in any other city but one, that economy could be brought about in these particulars. The same may be said with regard to rent, for Baltimore,

whose expenditures in this line are notorious, is the only city whose percentage exceeds Washington's. Coming back again to the defi ciency side of the table, small appropriations for evening schools have led a number of teachers to give their services voluntarily, and small appropriations for truant officers have led to voluntary activities in this regard as well. The figures demonstrate the need of increased appropriations for these last two purposes in order that Washington may have an organization which approximates the standard of other cities.

Comparison of percentages of any one city with like percentages of all cities of 30,000 population and over included in this study.-This may be done in the same manner as indicated above for comparison with cities in the same group by using the medians and the limits of the middle 50 per cent for all cities as presented in the following table: -Medians and limits of middle 50 per cents of percentages for entire list of 103

TABLE 3.

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The accompanying tables of distribution of percentages for the most important items for the entire list of cities make possible a comparison which shows more definitely the relation of any city to every other city as regards one particular item of expense. For example, suppose we wish to ascertain the relative position of Baltimore as regards the per cent of total expenses devoted to salaries of elementary teachers. By referring to Table 24, column 1, we note that the per cent for this purpose is 58.5. Then, by consulting Table 4 below, we ascertain that this per cent lies in the eighth step; that there are 18 cities in ali having per cents lying between 57.50 and 59.99; and that 66 cities have per cents lower than 57.50 and 17 cities have higher per cents than 59.99. These facts may be presented graphically in the same manner as a comparison of ratios of total expenses to population given in figure 8.

TABLE 4.-Distribution of percentages of total school expenses expended for various

purposes.

A. FOR SUPERINTENDENT'S OFFICE. (See Table 23, column 3.)

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C. SALARIES OF ELEMENTARY TEACHERS. (See Table 24, column 1.)

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D. TOTAL EXPENSES OF ELEMENTARY SCHOOLS. (See Table 24, column 13.)

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TABLE 4.--Distribution of percentages of total school expenses expended for various

purposes-Continued.

E. SALARIES OF SECONDARY TEACHERS. (See Table 25, column 1.)

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F. TOTAL EXPENSES OF SECONDARY SCHOOLS. (See Table 25, column 13.)

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G. SALARIES OF TEACHERS OF ALL SCHOOLS. (See Table 27, column 1.)

52.5 to 54.9.

55.0 to 57.4.

57.5 to 59.9.

60.0 to 62.4.

62.5 to 64.9.

65.0 to 67.4.

Less than 1.00..

1.00 to 1.99.

2.00 to 2.99.

3.00 to 3.99.

4.00 to 4.99.

5.00 to 5.99.

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H. SUPERVISION OF ALL SCHOOLS. (See Table 27, column 2.)

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8193

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17

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I. TEXT-BOOKS, STATIONERY, AND SCHOOL SUPPLIES OF ALL SCHOOLS. (See Table

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K. INSTRUCTION, OPERATION, AND MAINTENANCE OF ALL SCHOOLS. (See Table 27,

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