402 Life and Ijctters of Frnnch GoUon 



He sums up its merits as follows: 



"(1*) It eeUblishes a centesimal scale of precedence, into which the order of any individual, 

 in any army of individunlM and of any lenj^th, can be easily translated, and it gives the normal 

 deviate at the grade which the individual occupies. 



(2*) It easily defines the limiting values of successive classes of given numbers in a normal 

 amr. 



(8*) It classifies ohjwtfi that can be arrayed by judgment, though not by actual mojisurenient. 



(4*) It gives by inspection the value of <r [the standard deviation] in a normal series, and that 

 of the probable error in any seriep, whether normal or not. 



(5*) It exhibits processes under their reAl forms, and so is free from the danger of errors in 

 principle, to which those unpractised in statistics are liable. 



(6') It affords an excellent criterion as to whether an observed array is or is not normal, and 

 of the degree of its departure from normality." {\>. 104.) 



There is no doubt that Galton's method of grades and deviates will 

 retain a permanent position in statistics, chiefly as a means of illustrating in 

 a simple manner statistical results; but aa a fundamental method of tabula- 

 tion it cannot Ik? used. The ogive curve has no simple mathematical expres- 

 sion and data described in this way do not readily lend themselves to further 

 Quantitative discussion. This will be obvious to anyone who endeavours to 

 etermine the correlation coefficient from doubly-graded data, instead of 

 from a frequency table". Yet there was something fine about Galton's de- 

 fence of his first statistical method in his 85th ye-ar! It did not. perhaps, 

 convince the younger school, but it matlethem reconsider, and po.ssibly judge 

 more favourably and use more frequently, Galton's mode of representation. 



Some years earlier Galton reduced his method of determinuig the median 

 to a very simple process'. He transformed his "ogive ciu-ve " to a straight 

 line by altering its horizontal or percentile scale. He was thus applying to 

 a special case the conception of Lalanne's anamorphic geometry. In Galton's 

 case the scale of percentiles is so chosen that the vertical ordinate up to an 

 arbitrary sloping straight line represents the deviate in terms of the quartile 

 or standard deviation as unit. Percentiles 5° to 95° limit the practical range of 

 working. Any sloping straight line on this chart will be an ogive curve, i.e. 

 correspond to some one or other normal distribution. If we know that p^ per 

 cent, of individuals have a character less than A, anAjh per cent, a character 

 less than B, we plot A and B upwards at the percentiles p^ and jh respec- 

 tively, join by a straight line the tops of these ordinates, and the point in 

 whicli this line meets the 50" percentile gives by its ordinate the median. 

 I do not know whether Galton ever prepared an accurate chart ("abac") of 

 his ogive transformed to a line — I have not come across it — but it would not 

 be hard to do with considerable accuracy on a large scale, which might 

 then be reduced by photography to reasonable dimensions. 



Galton shows that linear interpolation on the ogive itself is very ini- 

 j)erfect unless p^ and p^ are equally distant from the 50" point. 



' Even the criterion suggested in (6°) is one rather of appearance than actual measure of 

 "goodness of fit." 



• "A Oeometric Determination of the Median Value of a System of Normal VariantH, from 

 two of iU Gentiles." Nature, Vol. Lxi, pp. 102-4, Nov. 30, 1899. 



