Statistics MCQs

Accountancy and Statistics

Statistics MCQs

Practice complete Statistics MCQs covering Primary & Secondary Data, Data Collection Methods, Questionnaire, Tabulation & Compilation of Data, Measures of Central Tendency, Probability, Theory of Attributes, Index Numbers, Demography, Census, Vital Statistics, Fertility Measures, and all other important topics. Includes chapter-wise and exam-oriented multiple choice questions with detailed answers and explanations for JKSSB, SSC, Banking, UPSC, CUET, University, and other competitive exams.

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Practice Questions

Page 22 of 66
Question #421
The harmonic mean of the numbers 3, 6, 9 is:
A. 54/11
B. 6
C. 11/54
D. 18/11
Discuss
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Correct Answer: Option A

Explanation:
HM = 3 / (1/3 + 1/6 + 1/9) = 3 / ( (6+3+2)/18 ) = 3 / (11/18) = 54/11 ≈ 4.909.
This question belongs to: Accountancy and Statistics Statistics
Question #422
Which measure of central tendency can be determined graphically from an ogive?
A. Mean
B. Mode
C. Median
D. Geometric mean
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Correct Answer: Option C

Explanation:
Median is the x-value corresponding to cumulative frequency N/2 on the ogive.
This question belongs to: Accountancy and Statistics Statistics
Question #423
The mean of a data set is 50 and the median is 52. Using the empirical relation, the approximate mode is:
A. 56
B. 44
C. 54
D. 48
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Correct Answer: Option A

Explanation:
Mode ≈ 3Median - 2Mean = 3×52 - 2×50 = 156 - 100 = 56.
This question belongs to: Accountancy and Statistics Statistics
Question #424
The geometric mean of 1, 2, 4, 8, 16 is:
A. 6
B. 4
C. 3.5
D. 5.2
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Correct Answer: Option B

Explanation:
Product = 1×2×4×8×16 = 1024. 1024^(1/5) = 4 (since 4^5=1024).
This question belongs to: Accountancy and Statistics Statistics
Question #425
The probability that a randomly chosen number from 1 to 100 is divisible by 7 or 11 is:
A. 20/100
B. 22/100
C. 25/100
D. 23/100
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Correct Answer: Option B

Explanation:
Multiples of 7: 14; of 11: 9; of 77: 1. Total = 14+9-1=22. P=22/100.
This question belongs to: Accountancy and Statistics Statistics
Question #426
Two cards are drawn from a deck without replacement. The probability that both are aces is:
A. 1/1326
B. 1/169
C. 1/221
D. 4/663
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Correct Answer: Option C

Explanation:
P = (4/52)×(3/51) = 12/2652 = 1/221.
This question belongs to: Accountancy and Statistics Statistics
Question #427
If a fair die is rolled twice, the probability that the first roll is a 4 and the second roll is a 5 is:
A. 1/18
B. 1/6
C. 1/12
D. 1/36
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Correct Answer: Option D

Explanation:
Independent events: (1/6)×(1/6)=1/36.
This question belongs to: Accountancy and Statistics Statistics
Question #428
Given P(A)=0.4, P(B)=0.5, and A and B are mutually exclusive, P(A∪B) is:
A. 0.1
B. 0.7
C. 0.2
D. 0.9
Discuss
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Correct Answer: Option D

Explanation:
Mutually exclusive ⇒ P(A∪B) = P(A)+P(B) = 0.4+0.5=0.9.
This question belongs to: Accountancy and Statistics Statistics
Question #429
If P(A)=0.6, P(B)=0.5, and P(A∩B)=0.3, then P(A'|B) is:
A. 0.2
B. 0.6
C. 0.5
D. 0.4
Discuss
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Correct Answer: Option D

Explanation:
P(A'|B) = 1 - P(A|B). P(A|B) = 0.3/0.5 = 0.6. So P(A'|B)=0.4.
This question belongs to: Accountancy and Statistics Statistics
Question #430
A box contains 4 white and 2 black balls. Two balls are drawn successively with replacement. Probability both are white is:
A. 5/9
B. 2/3
C. 1/9
D. 4/9
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Correct Answer: Option D

Explanation:
With replacement: P(WW) = (4/6)×(4/6) = 16/36 = 4/9.
This question belongs to: Accountancy and Statistics Statistics
Question #431
In a Poisson distribution, the probability of zero successes is e^{-λ}. If λ=3, this probability is approximately:
A. 0.15
B. 0.20
C. 0.05
D. 0.10
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Correct Answer: Option C

Explanation:
e^{-3} ≈ 0.0498 ≈ 0.05.
This question belongs to: Accountancy and Statistics Statistics
Question #432
If P(A)=0.7, P(B)=0.6, and the maximum possible value of P(A∩B) is 0.6, then the minimum possible value of P(A∪B) is:
A. 0.6
B. 0.8
C. 0.7
D. 1.0
Discuss
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Correct Answer: Option C

Explanation:
P(A∪B) = P(A)+P(B)-P(A∩B). To minimize union, maximize intersection: max=0.6. So min union = 0.7+0.6-0.6=0.7.
This question belongs to: Accountancy and Statistics Statistics
Question #433
Two events A and B are such that P(A)=0.5, P(B)=0.3, P(A∩B)=0.1. They are:
A. Independent
B. Neither mutually exclusive nor independent
C. Mutually exclusive
D. Both mutually exclusive and independent
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Correct Answer: Option B

Explanation:
P(A∩B)≠0 ⇒ not mutually exclusive. P(A)P(B)=0.15 ≠ 0.1 ⇒ not independent.
This question belongs to: Accountancy and Statistics Statistics
Question #434
A speaks truth in 60% cases, B in 70% cases. They agree in a statement. The probability that the statement is true is:
A. 0.42
B. 0.50
C. 0.78
D. 0.58
Discuss
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Correct Answer: Option C

Explanation:
Agreement can be both truth or both lie. P(both truth)=0.6×0.7=0.42; both lie=0.4×0.3=0.12. Total agreement=0.54. Probability truth given agreement = 0.42/0.54 ≈ 0.7778.
This question belongs to: Accountancy and Statistics Statistics
Question #435
For a given data, Σp₁q₀ = 600, Σp₀q₀ = 500, Σp₁q₁ = 700, Σp₀q₁ = 600. The value index is:
A. 116.67
B. 140
C. 120
D. 125
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Correct Answer: Option B

Explanation:
Value index = (Σp₁q₁ / Σp₀q₀) × 100 = 700/500 × 100 = 140.
This question belongs to: Accountancy and Statistics Statistics
Question #436
If the Laspeyres price index is 125 and Paasche price index is 115, the Fisher index is:
A. 119.83
B. 118.5
C. 121.0
D. 120.0
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Correct Answer: Option A

Explanation:
F = √(125×115) = √14375 ≈ 119.83.
This question belongs to: Accountancy and Statistics Statistics
Question #437
Which test of index numbers is violated by Laspeyres index?
A. Circular test
B. Unit test
C. Time reversal test
D. Factor reversal test
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Correct Answer: Option C

Explanation:
Laspeyres does not satisfy time reversal test; P₀₁(L) × P₁₀(L) ≠ 1.
This question belongs to: Accountancy and Statistics Statistics
Question #438
An index number constructed by taking the simple average of price relatives is called:
A. Simple average of relatives index
B. Chain index
C. Simple aggregative index
D. Weighted aggregative index
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Correct Answer: Option A

Explanation:
It is calculated as the arithmetic or geometric mean of individual price relatives.
This question belongs to: Accountancy and Statistics Statistics
Question #439
The CPI (Rural) and CPI (Urban) are compiled by:
A. NITI Aayog
B. Labour Bureau
C. RBI
D. Central Statistics Office (NSO)
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Correct Answer: Option D

Explanation:
The National Statistical Office (NSO), under MoSPI, compiles the CPI for rural, urban, and combined.
This question belongs to: Accountancy and Statistics Statistics
Question #440
If the WPI (base 2011-12) for March 2023 is 150, it means that wholesale prices have increased by ______ since base year.
A. 150%
B. 100%
C. 50%
D. 33.3%
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Correct Answer: Option C

Explanation:
Percentage increase = (150-100)/100 × 100 = 50%.
This question belongs to: Accountancy and Statistics Statistics

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