THEORY OF STATISTICS. 
EXERCISES. 
1. Take the following figures for girls corresponding to those for boys in 
Example i., p. 45, and discuss them similarly, but not necessarily using 
exactly the same comparisons, to see whether the conclusion that * the 
connecting link between defects of body and mental dulness is the coincident 
defect of brain which may be known by observation of abnormal nerve signs” 
seems to hold good. 
A, development defects. 2B, nerve signs. 2), mental dulness 
N 10,000 (4B) 248 
(4) 682 (4D) 307 
(B) 850 (BD) 363 
(D) 689 (4 BD) 128 
9. (Material from Census of England and Wales, 1891, vol, iii.) The 
following figures give the numbers of those suffering from single or combined 
infirmities : (1) for all males, (2) for males of 55 years of age and over. 
4, Blindness. B, Mental derangement. €, Deaf-mutism. 
(1) (2) (1) (2) 
All Males. Males 55- All Males. Males 55- 
N 14,053,000 1,377,000 (4B) 183 65 
(4) 12,281 5,538 (40) 51 14 
(B) 45,392 10,309 (BC) - 299 47 
(0) 7,707 746 (4BC) 11 3 
Tabulate proportions per thousand, exhibiting the total association between 
blindness and mental derangement, and the partial association between the 
same two infirmities among deaf-mutes, (1) for males in general, (2) for those 
of 55 years of age or over. Give a short verbal statement of the results, and 
contrast them with those of Question 1. 
3. (Material from supplement to 55th Annual Report Reg.-Genl.) 
The death-rate from cancer for occupied males in general (over 15) is 
0°685 per thousand per annum, and for farmers 120. 
The death-rates from cancer for occupied males under and over 45 respec- 
tively are 0°13 and 2°25 respectively. Of the farmers 46-1 per cent. are over 
45. 
Would you say that farmers were peculiarly liable to cancer? 
4. A population of males over 15 years of age consists of 7 per cent. over 65 
years of age and 93 per cent. under. The death-rates are 12 per thousand per 
annum in the younger class and 110 in the older, or 18-86 in the whole 
population. The death-rate of males (over 15) engaged in a certain industry 
is 267 per thousand. 
If the industry be not unhealthy, what must be the approximate proportion 
of those over 65 engaged in it (neglecting minor differences of age 
distribution) 
5. Show that if 4 and B are independent, while 4 and C, B and C are 
associated, 4 and B must be disassociated either in the universe of C's, 
the universe of v's, or both. 
6. As an illustration of Question 5, show that if the following were actual 
data, there would be a slight disassociation between the eye-colours of 
husband and wife (father and mother) for the parents either of light-eyed 
sons or not-light-eyed sons, or both, although there is a slight positive 
association for parents at large. 
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