THEORY OF STATISTICS. 
EXERCISES. 
1. (For this and similar estimates cf. ‘Report by Miss Collet on the 
Statistics of Employment of Women and Girls ” [C.—7564] 1894). If, in the 
urban district of Bury, 817 per thousand of the women between 20 and 25 
years of age were returned as ‘‘ occupied ” at the census of 1891, and 263 per 
thousand as married or widowed, what is the lowest proportion per thousand 
of the married or widowed that must have been occupied ? 
2. If, in a series of houses actually invaded by small-pox, 70 per cent. of the 
inhabitants are attacked and 85 per cent. have been vaccinated, what is the 
lowest percentage of the vaccinated that must have been attacked ? 
3. Given that 50 per cent. of the inmates of a workhouse are men, 60 per 
cent, are ‘‘ aged ” (over 60), 80 per cent. non-able-bodied, 85 per cent. aged 
men, 45 per cent. non-able-bodied men, and 42 per cent. non-able-bodied and 
aged, find the greatest and least possible proportions of non-able-bodied aged 
men. 
4. (Material from ref. 5 of Chap. I.) The following are the proportions 
per 10,000 of boys observed, with certain classes of defects amongst a number 
of school-children. 4 =development defects, B=nerve signs, D=mental 
dulness. 
N =10,000 (DY =739 
(4)= 877 (4B)=338 
(B)= 1,086 (BD)=455 
Show that some dull boys do not exhibit development defects, and state how 
many at least do not do so. 
5. The following are the corresponding figures for girls : — 
N =10,000 (D) =689 
(4)= 682 (4B)=248 
(B)= "850 (BD) =3863 
Show that some defectively developed girls are not dull, and state how many 
at least must be so. 
6. Take the syllogism “ All 4’s are B, all B’s are C, therefore all 4’s are 
C,” express the premisses in terms of the notation of the preceding chapters, 
and deduce the conclusion by the use of the general conditions of consistence. 
7. Do the same for the syllogism ‘‘ All 4’s are B, no B’s are C, therefore 
no 4’s are C.” 
8. Given that (4)=(B)=(C)=%4, and that (4B)/N=(4C)/N=p, find 
what must be the greatest or least values of p in order that we may infer 
that (BC)/N exceeds any given value, say g. 
9. Show that if ry & © 
4) _ = 2 
52 Fi 2% Nr 3z 
(4B)_(4C)_(BO)_ 
: ENE Ey 
the value of neither « nor 7 can exceed %. 
24 
nd