6iS 



NATURE 



[April 25, 1895 



ihe standard of difficulty of the papers set, the flatter is the mid 

 region of mediocrily. Fig. 2 shows the mean results of ten 

 separate examinations, of different students conducted by six 

 examiners, in history, English liteiature, geography, physical 

 geography, physics, botany, arithmetic, and Euclid. They are 

 taken without special selection from the returns of class 

 examinations in University College, Bristol. The standards 

 were somewhat markedly different ; in some the head, in others 

 ihe t.iil, being excessive ; hence the mid-region is not so 

 flattened as it probably would have been had a larger series 

 been taken. The results indicate, however, sufficiently well 



27 25 23 21 19 17 15 13 II 9 7 S 3 I 



Examinees. 



Fig. I. 



the general nature of the examination curve. The total range 

 of marks being from 175 per cent, to S4 per cent., 15 out of 

 the 30 students fall within the mid-region of from 40 per cent, 

 to 60 per cent. 



It is not my purpose to attempt to determine how far the 

 form of the lower end, or tail, of the curve is due to incapacity 

 on the one hand, or to sheer idleness on the other, and how far 

 that of ihe upper end, or head, of the curve is due lo exceptional 

 ability on the one hand, or to industry and hard work on the 

 other. Whichever cause preponderates, we may say that, at 

 any rale with pupils who have got beyond the school-boy stage. 



2a 27 2S 23 21 



£xamin\:es. 



Fig. 3. 



and very largely with them too, Ihe teacher's chief field of 

 influence is in the preponderant mid-region of mediocrily. 

 Those in the tail of the curve either cannot or will not profit by 

 hi« ministrations ; lho.se at Ihe head of the curve may be trusted 

 to do well without his aid, or even in spite of his interference. 

 It if on the body of the curve that he can do his best work. 



It is, at first sight, somewhat remarkable that the general 

 form of the curve persists as we ascend throu|>h a series of 

 graded examinations. It might well be supposed that the tail 

 would be eliminated in the lower examinations ; and the results 



NO. 1330 Vf L. 5ll 



of my own observations show that the tail does tend to flatten 

 out and become raised as we ascend. But it is by no means 

 got rid of. It flattens because we have eliminated the hope- 

 lessly idle and those who have altogether mistaken their 

 vocation. It persists because at each stage there are those 

 whose limils of capacity have been reached. .\ student whose 

 capacity may bring him into upper mediocrity in matriculation, 

 may drop hopelessly into the tail when he proceeds to work for 

 the degree. I was informed, on good authority, at the Cape, 

 that whereas the Kaffir lads were often ahead of white boys in 

 the early siages of education, the limits of their capacity were 

 soon readied, and they were left behind by those whom they 

 had before easily beaten. .\\. each stage there .ire pupils for 

 whom the work isbe)ond their powers ; and they inevitably fall 

 into the tail. 



In the traditional division of candidates into three classes, 

 the most rational method is to place in the first class those at 

 the head of the curve, the mediocrities in the second class, and 

 the tail in the Ihird class. For many years it has been my 

 custom as an examiner to plot out on the graphic method the 

 results of each examination. The advantage of doing so is 

 that one thus sees at a glance the distribution of the examinees. 

 One can also more leadily see where the divisions should run 

 between the several classes. It is irrational to fix beforehand 

 some arbitrary number i>f marks to form the limiting line above 

 which the candidates are to be called first class, those below 

 this and above another arbitrarily chosen number being ranked 

 in the second class. The limit must be de'ermined- -and even 

 then it is often only determined with difficulty — by an inspection 

 of the curve. The form of the curve, and the level of medio- 

 crity in ihe scale of marks, enable one to decide whether the 

 paper has been too hard or too easy. If too hard, the level of 

 mediocrily will be low, and the tail ir.ordinately large ; if too 

 easy, the level of mediocrily will be high, and the head not 

 well differentiated from the body. 



The examination curve may be commended to the special con- 

 sideration of those who have to deal with large numbers of 

 candidates in connection with the Education Department and 

 that for Science and Art. .\nd I would recommend to the con- 

 sideralion of these who have the control of Civil .Service and 

 .•\rmy Examinations the excellent suggestion made by Dr. J. 

 Venn, in a paper on the " Correlation of Mental and Physical 

 Powers," contributed to Ihe J/.'h/j/ for October 1S93. In these 

 examinations large numbers of candidates compete for a limited 

 number of v.icancies. Let the results be expressed in an 

 examination curve. It will have a well-marked head, a longish 

 body of mediocrity, and a decided tail. We may cheerfully 

 eliminate the tail ; it consists of duffers intellectually. We 

 m.ay select the head for entrance ; it consists of men of marked 

 intellectual superiorily, so far as the examinations are an adequate 

 test thereof. If the he.id exhausts all the vacancies, well and 

 good. But if the number of vacancies involves an extensive 

 incursion into the body of mediocrity, then it will be found 

 that the lower selected candidates will be very little superior 

 intellectually to the higher rejected candidates. The last ten 

 selected, and the ten seniors among the rejected, will piobahly 

 be separated by a comparatively small number of marks. 

 Moreover, it is a well-known fact, cxferlo cr^tie, thai, if, after 

 an extensive set of papers has been looked over and carefully 

 marked, an interval of time be allowed to elapse, and then the 

 papers are gone over again, the result of this re-examination is 

 that the head and tail remain practically unchanged, but that 

 there is not a little redistiilmlion among the mediocrities. 

 Furthermore, if a different examiner look over the papers, 

 the head and tail of his curve will not difler nitirkedly in 

 arrangement orfoim from those of his predecessor ; but among 

 the mediocrities there will be not a litlle shifting of places. 

 While, therefore, such an examination as that for entrance to 

 Woolwich or Sandhurst serves to select the intellectual he.ad,and 

 lo reject the intellectual tail, it is by no means so elTectual in 

 classifying the candidates who fall within the body of medio- 

 crity. 



Now if the same body of candidates be further examined by 

 some I hysical test (and Dr. Venn regards lung. capacity and 

 breathing power ihc best single physical test), it will be found 

 that in this resfcct theie will be a curve with well-inarkcd 

 hiad, a mediocre bcdy, and a lapidly descending tail. Hut the 

 inlcllcclual head and tail will not include the same candidates 

 as ihe physical head and tail. Let us therefore select from our 

 intellectual n.cdioctities those who fall within Ihe htad of the 



