GRADUATED TABLES-THIRD SERIES.

The following Table exhibits the ratio of the mean average attendance in each town to the whole number of children between 5 and 15, according to the returns. The mean average is found by adding the average attendance in Summer to the average attendance in Winter, and dividing the amount by 2. In some cases, the true mean average is not obtained by this process, for reasons peculiar to the schools of some towns. In such cases school committees were requested to indicate in their returns the true mean average, that their result may be inserted in the Table.

The ratio is expressed in decimals, continued to four figures, the first two of which are separated from the last two by a point, as only the two former are essential to denote the real per cent. Yet the ratios of many towns are so nearly equal, or the difference is so small a fraction, that the first two decimals, with the appropriate mathematical sign appended, indicate no distinction. The continuation of the decimals, therefore, is simply to indicate a priority in cases, where without such continuation, the ratios would appear to be precisely similar.

In several cases the ratio of attendance exhibited in the Table is more than 100 per cent. This result, supposing the registers to have been properly kept, and the returns correctly made, is to be thus explained:-the mean average attendance upon all the Public Schools, being compared with the whole number of children in the town between 5 and 15, the result may be over 100 per cent., because the attendance of children under 5 and over 15, may more than compensate for the absence of children between those ages.

Teachers and committees are sometimes not sufficiently careful to secure an accurate ret rn of the average attendance. On this account it is not claimed that the towns in all cases, are entitled to the exact precedence given them in the Table. They may not be thus entitled by the actual attendance, while they are so according to the

returns.

GRADUATED TABLES-THIRD SERIES.

Table, in which all the Towns in the State are numerically ar-
ranged, according to the AVERAGE ATTENDANCE of their children,
upon the Public Schools, for the year 1854–5.

* By referring to the Abstract of School Returns (page xvii.) it will be seen that the School Committee
of Phillipston return, as the "No. of Scholars of all ages in all the schools in Winter," 191; and an
average attendance" in Winter of 163 This shows the whole attendance to have been 9 more, and the
average attendance only 19 less than the whole number of persons between 5 and 15 years in the town, on
the 1st of May, added to the whole number attending school during the year under 5 and over 15!

+ The School Committee of Monroe return (page xxiv.) the whole attendance in Winter, 82, and the
average attendance 63. According to this return the whole attendance was 19 more than, and the aver
age attendance was exactly equal to, the whole number of persons between 5 and 15 in the town on the
1st of May, and to the whole number actually attending the schools, during the year, under 5 and
over 15!!

According to the Returns from Hopkinton (page xii.) the "No. of Scholars of all ages in all the
schools" in Winter, was 18 more than all the persons between 5 and 15 in the town on the previous
May, added to the whole number under 5 and over 15 actually atending school. Summer and Winter!
Such unusual results awaken an apprehension of incorrect returns, and that these towns, and perhaps
other towns may not be really entitled to the rank severally assigned them in this Table.