THEORY OF STATISTICS. 
(AB) and (4C), the conditions (4) give limits for the third, viz. 
(BC). They thus replace, for statistical purposes, the ordinary 
rules of syllogistic inference. From data of the syllogistic form, 
they would, of course, lead to the same conclusion, though in a 
somewhat cumbrous fashion; one or two cases are suggested as 
exercises for the student (Questions 6 and 7). The following 
will serve as illustrations of the statistical uses of the con- 
ditions :— 
Example i.—Given that (4)=(B)=(C)=1N and 80 per cent. 
of the 4’s are B, 75 per cent. of 4’s are C, find the limits to the 
percentage of B’s that are ¢'. The data are— 
2048) 2040) 
op 0-8 So = 0-75 
and the conditions give— 
HPL) e) 08 0 
(%) $0'8+075-1 
(c) 31 -08 +075 
(d) +1 +08 -075 
(a) gives a negative limit and (d) a limit greater than unity; 
hence they may be disregarded. From (6) and (¢) we have— 
280) AEC), ,. 
¥ 0°55 7 +095 
—that is to say, not less than 55 per cent. nor more than 95 per 
cent. of the B’s can be C. 
Erample ii.—If a report give the following frequencies as 
actually observed, show that there must be a misprint or mistake 
of some sort, and that possibly the misprint consists in the 
dropping of a 1 before the 85 given as the frequency (BC). 
& 1000 
(4) 510 (4B) 189 
(B) 490 (40) 140 
(®) 427 (BC) 85 
From (4) (a) we have— 
(BC) <510+490 +427 — 1000 — 189 — 140 
< 98. 
But 85 < 98, therefore it cannot be the correct value of (BC). 
If we read 185 for 85 all the conditions are fulfilled. 
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