400 A/'/f- an(f Lettcrx of Frimrin Gnlton 



The third memoir on horses also related to American trotters, but it is 

 14 yeiirs later, 1897'. In tliis paper Galt^)n draws attention to the value of the 

 speeds of the "trotters" and "pacers" in Wallace's Year Hook of Ann'i-ican 

 Trotters and suggests their importance for heredity. He notes, however, 

 that it is very ditncult to obtain the speeds of the parents and grandparents. 

 No liorse can theoretically obtain admittance to the trotting register unless 

 it can trot a mile in under 2 mins. 30 sees. The tlata, however, seem to indi- 

 cate either that some grace is given to horses who trot the distance of a mile 

 in a little over the limit time, or else that a good many ownei-s do not care to 

 press their homes beyond the limit of admission. In either case Galton was 

 justified in discarding the 2 mins. 29 sees, to 2 mins. 30 sees, entries <as not 

 homogeneous with the remainder. Dealing with the remainder Galton fits 

 the distribution by rather rough methods" with a j^ortion of a normal curve 

 of deviations, and thus is able to determine not only the mean speed but the 

 variation in the speed of American trotters. Thus he obtains for the median 

 and quartile of the series of 982 i-ecords for 1893, a median speed of 

 2 mins. 26 sees, with a quartile of 5 sees. (2 mins. 21 sees.). The paper is of 

 considemble value as it was. I believe, the first occasion on which an attempt 

 had been miule to fit incomplete series. 



(ii) The Median. There are a number of short papers by Galton which 

 are, perhaps, most suitably desilt with in this chapter. A good many of 

 them appeared in the pages of Nature, a ready means of attracting imme- 

 diate attention, but too often at the cost of later oblivion. Several of these 

 papers concern really important points, which have, since their publication, 

 oeen again and agiiin overlooked. 



In the firet place we may turn to a group dealing with the median or the 

 mid-character in a series. It is well-known that the median is subject to a 

 larger prolmble error than the mean and this has discouraged its use in 

 statistical inrjuiries dealing with carefully recorded observations. But Galton 

 realised that while its chief value in such cases was the rapidity with which 

 it could Im ascertained', yet there existed certain cjises in whicii the median 

 may be said to be far more reliable than the mean. In a paper of 1907 

 entitled " One Vote, One Value*," Galton draws attention to how misleading 

 a use of the averoijc may be. He cites as instfinces of importance anu 

 fretjuent occurrence: (i) the assessment by a jury of damsiges, (ii) tlie deter- 

 mination by the council of a society or by a committee of a sum of money 

 suitable for some particular purpose. Each voter, whether of jury or council, 

 ought to have equal authority with each of his colleagues. How can the 

 rigtit conclusion be drawn from the many individual estimates? Galton 



' Royal Soe. Proe. Vol. Lxn, pp. SlO-l."). See nXno Nature, Vol. Lvn, p. 333, Feb. 3, 1898. 



' More exact methods have Bincv been applied to the data: xoe liiometrika. Vol. n, pp. 2-G. 

 In the 1H93 case a mean of 2 niinH. 28 Hecs. and a quartile of 5*96 sees, were found. 



' That Oalton used median and (juartiles so frequently even on careful records must, I think, 

 l»e attribuUKl to his gn-at love of brief analysis. He found arithmetic in itself irksome; he 

 wduld prefer to int4-q>olat»' by a graph nither than by a formula, and while his rough approxima- 

 tiiins were as a rule justified, this was nut invariably the case. 



« Jfature, VoL uxv, p. 414, Feb. 28, 1907. 



