with Remarks on the Law of Frequency of Error. 35 



The next great point to be determined is the divergency of 

 the series — that is, the tendency of individual objects in it to 

 diverge from the mean value of all of them. The most conve- 

 nient measure of divergency is to take the object that has the 

 mean value, on the one hand, and those objects, on the other, 

 whose divergence in either direction is such that one half of the 

 objects in the series on the same side of the mean diverge 

 more than it does, and the other half less. The difference be- 

 tween the mean and either of these objects is the measure in 

 question, technically and rather absurdly called the " probable 

 error." Statisticians find this by an arithmetical treatment of 

 their numerous measurements ; I propose simply to take the 

 objects that occupy respectively the first and third quarter points 

 of the series. I prefer, on principle, to reckon the divergencies 

 in excess separately from those in deficiency. They cannot be 

 the same unless the series is symmetrical, which experience shows 

 me to be very rarely the case. It will be observed that my 

 process fails in giving the difference (probable error) in numerical 

 terms ; what it does is to select specimens whose differences 

 are precisely those we seek, and which we must appreciate as we 

 best can. 



We have seen how the mean heights &c. of two populations 

 may be compared ; in exactly the same way may we compare the 

 divergencies in two populations whose mean height is the same, 

 by collating representative men taken respectively from the first 

 and third quarter points of the series in each case. 



We may be confident that if any group be selected with the 

 ordinary precautions well known to statisticians, it will be so far 

 what may be called "generic" that the individual differences 

 of members of that group will be due to various combinations 

 of pretty much the same set of variable influences. Conse- 

 quently, by the well-known laws of combinations, medium values 

 will occur very much more frequently than extreme ones, the 

 rarity of the latter rapidly increasing as the deviation slowly in- 

 creases. Therefore, when the objects are marshalled in the order 

 of their magnitude along a level base at equal distances apart, 

 a line drawn freely through the tops of the ordinates which 

 represent their several magnitudes will form a curve of double 

 curvature. It will be nearly horizontal over a long space in the 

 middle, if the objects are very numerous ; it will bend down at 

 one end until it is nearly vertical, and it will rise up at the 

 other end until there also it is nearly vertical. Such a curve 

 is called, in the phraseology of architects, an " ogive," and is 

 represented by G in the diagram (fig. 1), in which the process of 

 statistics by intercomparison is clearly shown. If n= the length 

 of the base of the ogive, whose ordinate y represents the magni- 



D 2 



