Statistical Methods 37
on the method to be described in the next paragraph but one.
We are often called upon to define the position of an individual in his own series, in which case it is most conformable to usage to give his centesimal grade—that is, his place on the base line AB—supposing it to be graduated from 0° to 100° In reckoning this, a confusion ought to be avoided between “graduation” and “rank,” though it leads to no sensible error in practice. The first of the” park palings” does not stand at A, which is 0°, nor does the hundredth stand at B, which is 100°, for that would make 101 of them; but they stand at 0°.5 and 99°.5 respectively. Similarly, all intermediate ranks stand half a degree short of the graduation bearing the same number. When the class is large, the value of half a place becomes extremely small, and the rank and graduation may be treated as identical.
Examples of method of calculating a centesimal position
1. A child A is classed after examination as No. 5 in a class of 27 children; what is his centesimal graduation?
Answer.- If AB be divided into 27 graduations, his rank of No. will correspond to the graduation 40.5; therefore if AB be graduated afresh into 100 graduations, his centesimal grade, t; will be found by the Rule of Three, thus—
x : 4°.5 :: 100 : 27; x=459/27° = 16°.6.
2. Another child B is classed No. 13 in a class of 25.
Answer.—If AB be divided into 25 graduations, the rank of No. 13 will correspond to graduation 12°.5 whence as before—
x : 12°.5::100: 25; x = 1250/25° = 50°; i.e. B is the median.
The second method of comparing two statistical groups, to which I alluded in the last paragraph but one, consists in stating the centesimal grade in the one group that corresponds with the median or any other fractional grade in the other This, it will be remarked, is a very simple method of comparison, absolutely independent of any theory, and applicable to any statistical groups whatever, whether of physical or of mental qualities. Wherever we can sort in order, there we can apply this method. Thus, in the above examples, suppose A and B had been selected because they
