A PROPOSED STANDARDIZATION 547 



tions that mean and median values differ in the long run by but a 

 traction of one per cent, and if this be true, the only drawback of the 

 average deviation disappears. 



If then the average deviation, being sufficiently correct and more 

 easily computed, is accepted as the best measure of the accuracy of 

 a volume table it remains to be decided how it should be computed. 

 Several alternatives offer themselves. In the first place it must obvi- 

 ously be figured in percent and not (as in the foregoing table) in actual 

 differences, as otherwise relatively important errors in small trees would 

 have less weight than trivial errors in large. Secondly, it may be 

 calculated either from the average values of each diameter-height-class 

 (the results being properly weighted in accordance with the number 

 of trees in each class) or it may be computed for individual trees. The 

 use of the class averages will materially reduce the labor of computa- 

 tion, since they are usually worked out already in connection with the 

 preparation of the table, but it seems nevertheless inadvisable. It will 

 result in an artificially small average deviation and one which will 

 depend on the accident of the grouping of the trees in the size classes. 

 Of two volume tables, each based on the same number of trees, each 

 of the same range of size, and each with the same average deviation 

 by individual trees, that which has the greater concentration of tree 

 measurements into a few classes is almost certain to have the smaller 

 class-average deviation. This is because the class grouping permits 

 some plus and minus errors to offset each other, which is contrary to 

 the basic idea of the average deviation. There are cases, however, 

 as where volume tables are made from taper curves, where no other 

 procedure is practicable. Thirdly, it must be determined whether it is 

 necessary to interpolate between the actual values of the table to take 

 into account fractions of inches in diameter and fractions of logs in 

 height. While the average deviation should obviously be reduced by 

 this precaution, there is a great deal of work involved therein, and on 

 the whole it seems unnecessary. Its neglect should affect different 

 volume tables about equally regardless of the number of trees used or 

 their distribution. There should be a small handicap in favor of the 

 table which reads to every inch of diameter as compared with that 

 which reads only to even inches, or to every half log of height instead 

 of to every log, but this is a minor matter as compared to the great 

 additional labor involved in interpolations. 



