THEORY OF STATISTICS. 
8. The number of observations assigned to any class is termed, 
for brevity, the frequency of the class, or the class-frequency. 
Class-frequencies will be denoted by enclosing the corresponding 
class-symbols in brackets. Thus— 
(4) denotes number of A's, 1.6. objects possessing attribute 4 
(a) 7 ™ a’s, 2: DOG, on A 
(4B), ' AB's, ,» possessing attributes 4 and B 
(«B) 5 ” abB’s, ” ” »  Bbutnot 4 
(4BC) ,, 3 ABC's, 2 © ” A, B, and C 
(aBC) 2 aB(C’s, 2 >: B and C but not 4 
(BC) » aBC’s, ’ 2 » C but neither 4 nor B 
and so on for any number of attributes. If 4 represent, as in 
the illustration above, blindness, B deafness, C insanity, the 
symbols given stand for the numbers of the blind, the not-blind, 
the blind and deaf, the deaf but not blind, the blind, deaf, and vn- 
sane, the deaf and insane but mot blind, and the insane but neither 
blind nor deaf, respectively. 
9. The attributes denoted by capitals ABC, . .. may be 
termed positive attributes, and their contraries denoted by Greek 
letters negative attributes. If a class-symbol include only 
capital letters, the class may be termed a positive class; if only 
Greek letters, a negative class. Thus the classes 4, 4B, ABC 
are positive classes ; the classes a, af, ay, negative classes. 
If two classes are such that every attribute in the symbol for 
the one is the negative or contrary of the corresponding attribute 
in the symbol for the other, they may be termed contrary classes 
and their frequencies contrary frequencies ; e.g. 4B and of3, 4/8 
and aB, 43C and aBy, are pairs of contraries. 
10. The classes obtained by noting say = attributes fall into 
natural groups according to the numbers of attributes used to 
specify the respective classes, and these natural groups should be 
borne in mind in tabulating the class-frequencies. A class 
specified by r attributes may be spoken of as a class of the rth 
order and its frequency as a frequency of the th order. Thus 45, 
AC, BC are classes of the second order; (4), (48), (aBC), 
(4ByD), class-frequencies of the first, second, third, and fourth 
orders respectively. 
11. The classes of one and the same order fall into further 
groups according to the actual attributes specified. Thus if three 
attributes 4, B, C' have been noted, the classes of the second order 
may be specified by any one of the pairs of attributes 4B, AC, or 
BC (and their contraries). The series of classes or class-frequen- 
cies given by any one positive class and the classes whose symbols 
are derived therefrom by substituting Greek letters for one or 
more of the italic capital letters in every possible way will be 
termed an aggregate. Thus (4B) (43) (aB) (a3) form an aggre- 
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