Theory of Attributes: MCQs with Explanations
JKSSB FAA (Finance Accounts Assistant) Exam Practice
Q1. Consider the following statements regarding the Theory of Attributes:
1. The Theory of Attributes deals exclusively with qualitative characteristics that are classified into categories rather than measured numerically.
2. Every attribute necessarily has one and only one contrary attribute, and every individual must belong to exactly one of these two categories.
3. The contrary of an attribute is represented by the corresponding small Greek letter.
4. The presence of an attribute and its contrary can simultaneously exist for the same individual under exceptional circumstances.
(a) 1 and 3 only
(b) 1, 2 and 3 only
(c) 2 and 4 only
(d) 1, 2, 3 and 4
Answer: (b)
Explanation: Attributes are qualitative characteristics (honesty, literacy, blindness) that are classified, not measured. Under dichotomy, an attribute A (capital Latin letter) has one contrary α (small Greek letter), and every individual possesses either A or α. Statement 4 is wrong: an attribute and its contrary are mutually exclusive and can never coexist.
Q2. Which of the following are characteristics of ultimate class frequencies?
1. They are exhaustive.
2. They are mutually exclusive.
3. Their total equals the universe.
4. They overlap with each other.
(a) All of the above
(b) 2, 3 and 4 only
(c) 1, 2 and 3 only
(d) 1 and 4 only
Answer: (c)
Explanation: Ultimate class frequencies are exhaustive, mutually exclusive, and together add up to the universe (N). They never overlap.
Q3. Consider the following statements with reference to three attributes A, B & C:
1. The ultimate classes are ABC, ABγ, AβC, Aβγ, αBC, αBγ, αβC, αβγ.
2. Every individual in the population belongs to one and only one ultimate class.
3. The sum of all ultimate class frequencies is equal to the total frequency N.
4. The ultimate classes are mutually exclusive as well as collectively exhaustive.
(a) 1, 2 and 3 only
(b) 1, 3 and 4 only
(c) 1, 2, 3 and 4
(d) 2, 3 and 4 only
Answer: (c)
Explanation: For n attributes there are 2ⁿ ultimate classes; for 3 attributes, 2³ = 8 classes (all listed in statement 1). They are mutually exclusive and exhaustive, so each individual falls in exactly one and the frequencies sum to N.
Q4. If the value of Q is 1, then the value of (Ab) is:
(a) 1
(b) 0
(c) Infinite
(d) None of these
Answer: (b)
Explanation: Yule's coefficient of association Q = [(AB)(ab) − (Ab)(aB)] / [(AB)(ab) + (Ab)(aB)] lies between −1 and +1. Q = +1 means complete positive association, which happens when (Ab) = 0 or (aB) = 0. (For Q = −1, (AB) = 0 or (ab) = 0.)
Q5. Which of the following statements are true?
1. Total frequency is known as the universe.
2. Class frequency cannot exceed the total frequency.
3. Ultimate class frequencies are obtained after considering all attributes.
(a) 1 only
(b) 2 and 3 only
(c) 1, 2 and 3
(d) 1 and 3 only
Answer: (c)
Explanation: The universe (N) is the total frequency. A class is a part of the universe, so its frequency cannot exceed N. Ultimate class frequencies are those of the highest order, where all attributes under study are specified.
Q6. Match List-I with List-II and select the correct answer using the codes given below.
List-I (Characteristic): A. Eye Colour; B. Height; C. Literacy Status; D. Blood Group
List-II (Classification): 1. Variable; 2. Attribute; 3. Quantitative Characteristic; 4. Qualitative Characteristic
(a) A-2, B-1, C-4, D-3
(b) A-4, B-3, C-2, D-1
(c) A-2, B-3, C-4, D-2
(d) A-4, B-1, C-2, D-3
Answer: (c)
Explanation: Eye colour and blood group are attributes (qualitative, classified into categories). Height is measured numerically, so it is a quantitative characteristic. Literacy status is a qualitative characteristic.
Q7. Consider the following statements regarding the classification of attributes:
1. In the classical Theory of Attributes, an attribute generally divides the population into two mutually exclusive classes based on its presence or absence.
2. Such a two-class classification is known as dichotomous classification.
3. If an attribute divides the population into more than two classes, the classification is known as manifold classification.
4. A trichotomous classification is a special case of manifold classification in which the population is divided into exactly two classes.
(a) 1 and 2 only
(b) 1, 2 and 3 only
(c) 2, 3 and 4 only
(d) 1, 2, 3 and 4
Answer: (b)
Explanation: Two classes = dichotomy; more than two = manifold classification. Statement 4 is wrong: trichotomy divides the population into exactly THREE classes, not two.
Q8. Consider the following statements regarding the order of classes in the Theory of Attributes:
1. The total frequency of the universe, denoted by N, is regarded as the frequency of the class of zero order.
2. A first-order class frequency is obtained by considering the presence or absence of only one attribute.
3. A second-order class frequency involves the simultaneous specification of two attributes.
4. The order of a class depends on the number of individuals contained in that class rather than on the number of attributes specified.
(a) 1, 2 and 3 only
(b) 1 and 4 only
(c) 2 and 3 only
(d) 1, 2, 3 and 4
Answer: (a)
Explanation: Order = number of attributes specified. N is of zero order; (A), (α) are first order; (AB), (Aβ) are second order. Statement 4 is wrong: order depends on the number of attributes, not on the number of individuals.
Q9. Assertion (A): (AB)(αβ) > (Aβ)(αB).
Reason (R): Positive association implies that the joint occurrence of the two attributes is greater than expected under independence, resulting in the product of concordant frequencies exceeding the product of discordant frequencies.
(a) Both A and R are true, and R is the correct explanation of A
(b) Both A and R are true, but R is not the correct explanation of A
(c) A is true, but R is false
(d) A is false, but R is true
Answer: (a)
Explanation: Attributes A and B are positively associated when (AB) > (A)(B)/N, which is equivalent to (AB)(αβ) > (Aβ)(αB). So R explains A. The inequality (AB)(αβ) > (Aβ)(αB) is the condition for positive association (Q > 0).
Q10. If for two attributes the class frequencies (AB)(αβ) = (Aβ)(αB), then Q is equal to:
(a) 0
(b) −1
(c) +1
(d) Infinite
Answer: (a)
Explanation: Q = [(AB)(αβ) − (Aβ)(αB)] / [(AB)(αβ) + (Aβ)(αB)]. If the two products are equal, the numerator is 0, so Q = 0, meaning the attributes are independent (no association).
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