Stattnticfil InveHtigaliotia 401 



holds, iiiid surely he 18 rij'ht, that the muldlemoat eHtinutte, the median, is 

 the correct out*. Every other estimate has a majority of the voters against 

 it as either t<K) low or too high. The correct estimate cannot be the average 

 tor, as Galtori puts it, the average "j^ives a voting power to 'cranks' in 

 |)rofX)rtion to their crankiness." The average allows crankiness to swamp 

 leasonahle judgment. Vor such reasons Galton laid considenihle stress on 

 the nu'dian, and on various contrivances for ra{)idly determining it. 



1 have already referrtid (pp. ^36, 385) to the use Galton made of two bows 

 or two weights to test the strength of a eroup, and how he determined his 

 median from the resulting percontagea This point is more fully dealt with 

 in a paper on "The Median Estimate" read at the Dover meeting of the 

 British A.ssociation in 1891)'. In this paper Galton applies the two weights 

 test to determine the ])roper damages by a jury or a suitable grant by a 

 committee. Two sums A and B, li Ix'iiig greater than A, are tixed on and 

 then three shows or counts of hands are taken, (i) for a sum less than A, 

 (ii) for a sum between .el and li, and (iii) for a simi gi-eater than B. The 

 individuals have thus not to determine actual amounts, but only inequalities. 

 Galton now assumes the "normal" distribution of judgments and proceeds 

 to determine the median in the manner of our footnote, p. 385'. To ex- 

 pedite the determination he pul)lished a table of percentiles giving the 

 ordinates in terms of the quartile. This table is also reprofluced in a paper 

 of the following year and originally appeared in his lx)ok Natural Innent- 

 ann- of 1889. It can still be usetl although it only gives three signiticant 

 tigures (two decimals), when the quartile is preferred. It has, however, 

 been superseded for most ptn-poses l)y the table of five significant figtn*e8 

 (tour decimals) provide<l by I)r W. F. Sheppard at the 8ugge.stion of (ialton, 

 who wrote a prefatory note to the table*. This table gives the deviate in 

 terms of the standai'd deviation and proceeds by permilles not percentile.s. 

 The prefatory note is a remarkaljle one considering that Galton was then 

 aged 85; he there broke a last lance for the use of the ogive curve and the 

 median, which he had introduced 40 years earlier. He took his present 

 biographer's data for the intelligence of Cambridge graduates and repre- 

 sented it on a percentile scale and not on the biograplier's "normal" scale; 

 and he made a very good defence of his method. 



' British Asgociatton Report, 1899, pp. 638—40. 



' If 6 and a be the fractions of the total assessors who vote "above ^"and "below A" respec- 

 tively, then the ordinate's of the probability curve corresponding to h and a, in terms of the 

 standard deviation as unit, can 1k^ found from a table of permilles (see TcM«* for Statitticiafu 

 and Biometrician,^, Table I). If these be a and /3 the median will be 



. B-A „ .B-A 

 m = A+a ^ = B—p -_ . 



Here we suppose a and 6 both less than 50 per cent, of the total number of  M e na ofB. This is the 

 Ixitter way of determining to; a slight modification is neede<l, if m be greater (or less) than both 

 A and B. The values of a and b should correspond U^ n\oro than 5 i>er cent, of the asses-sors 

 for reasonable accuracy. 



' Biometrika, Vol. v, pp. 400-6. "Grades and Deviates (including a Table of Normal 

 Deviates corresponding to each millesimal grade in the length of an array, and a figure)." 



ran 61 



