8) a) What is meant by a class frequency of (i) first order (ii) third order? How would you express a class
frequency of first order in terms of class frequencies of higher orders? [6]
b) If a collection contains N items, each of which is characterized by one or more of the attributes A,
B, C and D. Show that with the usual notations [3+3]
(i) () ≥ () + () + () + () − 3
(ii) () ≥ () + () − () + ()
Where , represent the characteristics of the absence of B and C respectively.
Answers
Order of class and class frequency ... representing one attribute is called a class of first order. Thus, A, B, C, ... case of two attributes class-frequencies of order two are ultimate.
A Class is generally termed as the category of attributes. Their frequency is called the class frequency. For attributes that are dichotomous, the class frequencies are called positive class when the attributes are present and it is called negative class during the absence of attributes.
A first-order frequency is one that consists of attributes of order one. These are denoted as single Greek letters. The positive class is denoted by A, B, C.. and the negative class is usually denoted by α, β,, γ and so on.
Similarly, a third-order class frequency has attributes of third order and is generally represented as ABC, ABγ, αβC and so on.
The class frequency of first order can be expressed in terms of class frequency of higher order by sum of high order frequency cells:
for A and B
N = (A)+ (B) + (α) + (β)
(A)= (AB) + (Aβ) and (α) = (αB) + (αβ)
(B= (AB) +(αB) and (β) = (Aβ)+ (Bβ) and so on. this way higher-order class frequencies can be represented by first-class frequencies
(ABCD) ≥ (ABC) + (BCD) + (CDA) + (DAC)
(D) ≥ (A) + (B) - (N) + (C)
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