Statistics MCQs

Question #61

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Which measure of central tendency is most suitable for qualitative ordinal data like intelligence rankings?

A. Geometric mean

B. Mean

C. Mode

D. Median

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Correct Answer: Option D

Explanation:
Ordinal data can be ranked; the median is the appropriate measure as it does not require numerical differences.

This question belongs to: Accountancy and Statistics Statistics

Question #62

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In a frequency distribution, the modal class is the class with:

A. Highest frequency

B. Median value

C. Highest class mark

D. Largest class interval

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Correct Answer: Option A

Explanation:
The mode is the most frequent value; the modal class is the interval with the maximum frequency.

This question belongs to: Accountancy and Statistics Statistics

Question #63

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If in a moderately skewed distribution mean = 30 and median = 28, the empirical mode is approximately:

A. 24

B. 22

C. 32

D. 26

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Correct Answer: Option A

Explanation:
Using the empirical relation: Mode ≈ 3Median - 2Mean = 3×28 - 2×30 = 84 - 60 = 24.

This question belongs to: Accountancy and Statistics Statistics

Question #64

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If a die is rolled, the sample space is:

A. {1,2,3,4,5,6}

B. {0,1,2,3,4,5,6}

C. {2,4,6}

D. {1,2,3,4,5}

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Correct Answer: Option A

Explanation:
A fair die has six possible outcomes: 1,2,3,4,5,6.

This question belongs to: Accountancy and Statistics Statistics

Question #65

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If P(A)=0.5, P(B)=0.4, and P(A∩B)=0.2, then P(A∪B) equals:

A. 0.9

B. 0.7

C. 0.2

D. 0.5

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Correct Answer: Option B

Explanation:
By addition theorem: P(A∪B) = P(A) + P(B) - P(A∩B) = 0.5 + 0.4 - 0.2 = 0.7.

This question belongs to: Accountancy and Statistics Statistics

Question #66

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Conditional probability P(A|B) is defined as:

A. P(A∩B) / P(A)

B. P(A∩B) / P(B)

C. P(A) / P(B)

D. P(B) / P(A)

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Correct Answer: Option B

Explanation:
P(A|B) = P(A∩B) / P(B), provided P(B) > 0.

This question belongs to: Accountancy and Statistics Statistics

Question #67

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A box contains 5 red and 3 green balls. Two balls are drawn without replacement. Probability that both are red is:

A. (5/8) × (3/7)

B. (5/8)²

C. (5/8) × (4/7) = 5/14

D. (5/8) + (4/7)

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Correct Answer: Option C

Explanation:
First red: 5/8, second red given first red: 4/7. Product = 20/56 = 5/14.

This question belongs to: Accountancy and Statistics Statistics

Question #68

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In a factory, machine A produces 60% of items (defective 2%) and machine B 40% (defective 5%). If an item is defective, the probability it came from B is:

A. 0.375

B. 0.625

C. 0.5

D. 0.8

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Correct Answer: Option B

Explanation:
Bayes: P(B|D)= (0.05×0.4)/(0.02×0.6 + 0.05×0.4) = 0.02/0.032 = 0.625.

This question belongs to: Accountancy and Statistics Statistics

Question #69

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Which of the following is a valid probability value?

A. 0.75

B. 2

C. 1.5

D. -0.2

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Correct Answer: Option A

Explanation:
Probability must lie between 0 and 1 inclusive. 0.75 is valid.

This question belongs to: Accountancy and Statistics Statistics

Question #70

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In the theory of attributes, the class frequency (AB) denotes:

A. Number of objects possessing attribute A only

B. Number of objects possessing both A and B

C. Number of objects not possessing A and B

D. Number of objects possessing attribute B only

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Correct Answer: Option B

Explanation:
The notation (AB) represents the number of items possessing both attributes A and B.

This question belongs to: Accountancy and Statistics Statistics

Question #71

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If A and B are two attributes, the symbol (α) denotes:

A. Number possessing both A and B

B. Number not possessing attribute A

C. Number possessing neither A nor B

D. Number possessing attribute A

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Correct Answer: Option B

Explanation:
α (alpha) is the negation of A; (α) is the number of items that do not possess attribute A.

This question belongs to: Accountancy and Statistics Statistics

Question #72

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For two attributes A and B, independence (no association) implies:

A. (AB) = (A)(B)/N²

B. (AB) = (A) + (B)

C. (AB)/N = (A)/N × (B)/N

D. (AB) = 0

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Correct Answer: Option C

Explanation:
Independence means the proportion of items with both attributes equals the product of the individual proportions.

This question belongs to: Accountancy and Statistics Statistics

Question #73

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Given N=100, (A)=40, (B)=30. The expected frequency of (AB) under independence is:

A. 20

B. 40

C. 30

D. 12

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Correct Answer: Option D

Explanation:
Expected (AB) = (A)×(B)/N = 40×30/100 = 12.

This question belongs to: Accountancy and Statistics Statistics

Question #74

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Which of the following is a necessary condition for consistency of data for two attributes?

A. All of these

B. (AB) ≥ 0

C. (A) ≥ (AB)

D. (αβ) ≥ 0

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Correct Answer: Option A

Explanation:
All ultimate class frequencies must be non-negative, and marginal conditions like (A) ≥ (AB) must hold.

This question belongs to: Accountancy and Statistics Statistics

Question #75

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Laspeyres price index uses weights of:

A. Current period quantities

B. Base period quantities

C. Fixed arbitrary weights

D. Average of base and current quantities

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Correct Answer: Option B

Explanation:
Laspeyres index is Σ(p₁q₀)/Σ(p₀q₀) × 100, using base period quantities as weights.

This question belongs to: Accountancy and Statistics Statistics

Question #76

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Paasche's price index formula is:

A. Σp₁q₁ / Σp₀q₀ × 100

B. Σp₁q₀ / Σp₀q₀ × 100

C. Σp₁q₁ / Σp₀q₁ × 100

D. Σp₁(q₀+q₁) / Σp₀(q₀+q₁) × 100

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Correct Answer: Option C

Explanation:
Paasche index uses current period quantities: Σp₁q₁ / Σp₀q₁ × 100.

This question belongs to: Accountancy and Statistics Statistics

Question #77

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Fisher's ideal index satisfies which tests?

A. Both time reversal and factor reversal tests

B. Circular test

C. Time reversal test only

D. Factor reversal test only

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Correct Answer: Option A

Explanation:
Fisher's index is the geometric mean of Laspeyres and Paasche and satisfies both the time reversal and factor reversal tests.

This question belongs to: Accountancy and Statistics Statistics

Question #78

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Which of the following indices does NOT satisfy the time reversal test?

A. Paasche index

B. Fisher index

C. Laspeyres index

D. Both Laspeyres and Paasche

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Correct Answer: Option D

Explanation:
Laspeyres and Paasche indices fail the time reversal test; Fisher's index satisfies it.

This question belongs to: Accountancy and Statistics Statistics

Question #79

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Compute Fisher's ideal index from: Σp₀q₀=200, Σp₀q₁=250, Σp₁q₀=300, Σp₁q₁=360.

A. 146.97

B. 145.5

C. 147.0

D. 146.0

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Correct Answer: Option A

Explanation:
Laspeyres = 300/200×100=150. Paasche = 360/250×100=144. Fisher = √(150×144) = √21600 ≈ 146.97.

This question belongs to: Accountancy and Statistics Statistics

Question #80

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The Wholesale Price Index (WPI) in India is compiled by:

A. Office of Economic Adviser, DPIIT

B. RBI

C. NSSO

D. CSO

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Correct Answer: Option A

Explanation:
The Office of the Economic Adviser in the Department for Promotion of Industry and Internal Trade (DPIIT) compiles WPI.

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