400 
THEORY OF STATISTICS. 
CHAPTER III. 
1. Deaf-mutes from childhood per million among males 222; among 
females 183 ; there is therefore positive association between deaf-mutism and 
male sex : if there had been no association between deaf-mutism and sex, there 
would have been 3176 male and 3393 female deaf-mutes. 
2. (a) positive association, since (4.B),=1457. 
(b) negative association, since 294/490=3/5, 380/570 =2/3. 
(¢) independence, since 256/768 =1/3, 48/144=1/3. 
2 Percentage of Plants above the Average Height, 
Parentage Crossed. Self-fertilised. 
Ipomea purpurea. : . . 86 per cent. 25 per cent. 
Petunia violacea . . EE 17 a 
Reseda lutea . . Sa Dahl 
Reseda odorata . . «571 AT 
Lobelia fulgens . : i500 + 35 a 
The association is much less for the species at the end than for those at the 
beginning of the list. 
4, Percentage of dark-eyed amongst the sons of dark-eyed fathers 39 per 
cent. 
Percentage of dark-eyed amongst the sons of not dark-eyed fathers 10 per 
cent. 
If there had been no heredity, the frequencies to the nearest unit would 
have been (4B), 18, (48), 111, (aB), 121, (aB), 750. 
5. Percentage of light-eyed amongst the wives of light-eyed husbands 59 
per cent. 
Percentage of light-eyed amongst the wives of not light-eyed husbands 53 
per cent, 
If there had been no association : (4B),=298, (AB),=225, (aB)y=143, (aB), 
=1108. 
6. The following are the proportions of the insane per thousand in 
successive age groups :— 
In general population: 09, 2-3, 41, 57, 69, 7°5, 727,16:8. 
Amongst the blind : 20-1, 160,.16°3, 20:7, 18:3, 17-8, 114, 5°3. 
Note the diminishing association, which is especially clear in the age-group 
65—, and the negative association in the last age-group The association 
coefficient gives the values below, which decrease continuously :— 
Association coefficient: +092, +075, +0°61, +057, +046, +0°41, 
+020, — 0°13. 
CHAPTER IV. 
1. (D)/N = 6°9 per cent. (4)/N = 6-8 per cent. 
(AD)j(4) =450 (AD)(D) =446 
(BD)/(B) = 86 (4p)/(B) = &T 
(48D)/(4B) =412 ,, (4BD)/(BD) =54'9 
(BD)/(B) =42T (4B)[(B) =292 
(4BD)/(AB)=516 ,, (4BD)/(BD)=85'3 ,, 
The above give two legitimate comparisons. The general results are the same 
as for the boys, ¢.e. a very small association between development-defects and 
dulness amongst those exhibiting nerve-signs, as compared with those who do