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 57 of 66
Question #1121
In a moderately skewed distribution, if the mean is 45 and the mode is 39, the median is approximately:
A. 43
B. 44
C. 42
D. 41
Discuss
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Correct Answer: Option A

Explanation:
Using the empirical relationship: Mode ≈ 3×Median - 2×Mean. Rearranging: Median ≈ (Mode + 2×Mean)/3 = (39 + 90)/3 = 129/3 = 43. This approximation holds for moderately skewed unimodal distributions.
This question belongs to: Accountancy and Statistics Statistics
Question #1122
Which measure of central tendency can be used for both quantitative and qualitative (nominal) data?
A. Arithmetic mean
B. Median
C. Mode
D. Geometric mean
Discuss
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Correct Answer: Option C

Explanation:
The mode identifies the most frequent category and can be applied to nominal qualitative data (e.g., favorite color), whereas mean and median require at least ordinal or numerical data.
This question belongs to: Accountancy and Statistics Statistics
Question #1123
A random experiment is defined as:
A. An experiment where all outcomes are equally likely
B. An experiment conducted only once
C. An experiment that can be repeated under identical conditions with uncertain outcomes
D. An experiment with a predetermined outcome
Discuss
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Correct Answer: Option C

Explanation:
A random experiment has well-defined possible outcomes, can be repeated under similar conditions, and the exact outcome cannot be predicted with certainty before performing the experiment.
This question belongs to: Accountancy and Statistics Statistics
Question #1124
The sample space for tossing two fair coins is:
A. {HH, HT, TH, TT}
B. {0, 1, 2}
C. {H, T}
D. {2H, 1H1T, 2T}
Discuss
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Correct Answer: Option A

Explanation:
The sample space lists all possible distinct outcomes; for two coin tosses, the outcomes are HH, HT, TH, and TT, representing the sequence of heads (H) and tails (T).
This question belongs to: Accountancy and Statistics Statistics
Question #1125
The addition theorem of probability for two events A and B states that P(A ∪ B) = P(A) + P(B) - P(A ∩ B). This formula accounts for:
A. The double-counting of outcomes common to both A and B
B. The complement of event A
C. The conditional probability of A given B
D. The independence of events
Discuss
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Correct Answer: Option A

Explanation:
Subtracting P(A ∩ B) corrects for the fact that outcomes in the intersection are counted twice when adding P(A) and P(B), ensuring accurate probability calculation for the union.
This question belongs to: Accountancy and Statistics Statistics
Question #1126
If P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2, then P(A|B) is:
A. 0.2
B. 0.8
C. 0.4
D. 0.5
Discuss
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Correct Answer: Option C

Explanation:
Conditional probability P(A|B) = P(A ∩ B) / P(B) = 0.2 / 0.5 = 0.4. This represents the probability of A occurring given that B has already occurred.
This question belongs to: Accountancy and Statistics Statistics
Question #1127
Bayes' theorem is primarily used to:
A. Compute the expected value of a random variable
B. Calculate the probability of the union of events
C. Update the probability of a hypothesis based on new evidence
D. Determine if two events are mutually exclusive
Discuss
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Correct Answer: Option C

Explanation:
Bayes' theorem allows revising prior probabilities of hypotheses in light of new data or evidence, making it fundamental in statistical inference and decision-making under uncertainty.
This question belongs to: Accountancy and Statistics Statistics
Question #1128
A bag contains 3 red and 2 blue balls. Two balls are drawn at random without replacement. The probability that both are red is:
A. 9/25
B. 3/5
C. 3/10
D. 1/2
Discuss
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Correct Answer: Option C

Explanation:
P(both red) = (3/5) × (2/4) = 6/20 = 3/10. Without replacement, the probability changes after the first draw, requiring multiplication of conditional probabilities.
This question belongs to: Accountancy and Statistics Statistics
Question #1129
If the probability that a student passes Mathematics is 0.7, passes English is 0.6, and passes both is 0.4, what is the probability that the student passes at least one subject?
A. 0.8
B. 0.9
C. 1.0
D. 0.7
Discuss
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Correct Answer: Option B

Explanation:
P(Math ∪ English) = P(Math) + P(English) - P(both) = 0.7 + 0.6 - 0.4 = 0.9. This uses the addition theorem to avoid double-counting students who pass both.
This question belongs to: Accountancy and Statistics Statistics
Question #1130
Assertion (A): For independent events A and B, P(A|B) = P(A). Reason (R): Independence implies that knowledge of B does not change the probability of A.
A. Both A and R are true, but R is not the correct explanation of A
B. A is true but R is false
C. Both A and R are true, and R is the correct explanation of A
D. A is false but R is true
Discuss
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Correct Answer: Option C

Explanation:
By definition, if A and B are independent, the conditional probability P(A|B) equals the unconditional probability P(A), as the occurrence of B provides no information about A.
This question belongs to: Accountancy and Statistics Statistics
Question #1131
In a factory, machines A, B, and C produce 30%, 45%, and 25% of total output, with defect rates of 2%, 3%, and 4% respectively. If a randomly selected item is defective, the probability it was produced by machine B is approximately:
A. 0.50
B. 0.43
C. 0.30
D. 0.45
Discuss
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Correct Answer: Option B

Explanation:
Using Bayes' theorem: P(B|Defective) = [P(Defective|B) × P(B)] / [Σ P(Defective|machine) × P(machine)] = (0.03×0.45) / (0.02×0.30 + 0.03×0.45 + 0.04×0.25) = 0.0135 / 0.0315 ≈ 0.4286 ≈ 0.43.
This question belongs to: Accountancy and Statistics Statistics
Question #1132
The theory of attributes deals with data that is:
A. Qualitative and categorical
B. Time-series based
C. Spatially distributed
D. Quantitative and continuous
Discuss
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Correct Answer: Option A

Explanation:
Theory of attributes focuses on qualitative characteristics (attributes) that classify units into categories, such as literacy (literate/illiterate) or gender (male/female), rather than numerical measurements.
This question belongs to: Accountancy and Statistics Statistics
Question #1133
In attribute classification, a 'positive attribute' refers to:
A. The presence of a characteristic, denoted by a capital letter (e.g., A for literate)
B. An attribute with only two possible categories
C. An attribute that is desirable or beneficial
D. An attribute that always has a numerical value greater than zero
Discuss
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Correct Answer: Option A

Explanation:
In statistical notation for attributes, a positive attribute (e.g., A) denotes the presence of a characteristic, while its absence is denoted by the corresponding Greek letter (e.g., α for illiterate).
This question belongs to: Accountancy and Statistics Statistics
Question #1134
Ultimate class frequencies in a three-attribute system (A, B, C) refer to frequencies of classes like:
A. (A), (B), (C)
B. N only
C. (AB), (AC), (BC)
D. (ABC), (ABγ), (AβC), (αBC), etc.
Discuss
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Correct Answer: Option D

Explanation:
Ultimate class frequencies are the most detailed categories where each unit is classified by the presence or absence of every attribute, e.g., (ABC) for possessing all three, (ABγ) for A and B present but C absent.
This question belongs to: Accountancy and Statistics Statistics
Question #1135
Data on attributes is said to be consistent if:
A. The sum of all frequencies equals the sample size
B. No calculated class frequency is negative, as negative frequencies are impossible
C. All class frequencies are positive integers
D. Attributes are independent of each other
Discuss
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Correct Answer: Option B

Explanation:
Consistency requires that all derived class frequencies (including ultimate classes) are non-negative, as negative counts are logically impossible in real-world data.
This question belongs to: Accountancy and Statistics Statistics
Question #1136
Yule's coefficient of association (Q) for attributes A and B ranges between:
A. -1 and +1
B. 0 and N
C. -∞ and +∞
D. 0 and 1
Discuss
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Correct Answer: Option A

Explanation:
Yule's Q = [(AB)(αβ) - (Aβ)(αB)] / [(AB)(αβ) + (Aβ)(αB)], which ranges from -1 (perfect negative association) to +1 (perfect positive association), with 0 indicating independence.
This question belongs to: Accountancy and Statistics Statistics
Question #1137
A study records literacy (A) and employment (B) in a population of 1000. Given (A)=600, (B)=700, (AB)=450. The coefficient of association suggests:
A. Negative association
B. Perfect positive association
C. Positive association
D. No association (independence)
Discuss
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Correct Answer: Option C

Explanation:
Expected (AB) under independence = (600×700)/1000 = 420. Observed (AB)=450 > 420, indicating positive association. Yule's Q = [(450×150) - (150×250)] / [(450×150) + (150×250)] = (67500-37500)/(67500+37500)=30000/105000≈0.286, confirming positive but not perfect association.
This question belongs to: Accountancy and Statistics Statistics
Question #1138
Assertion (A): Association between attributes does not imply causation. Reason (R): Two attributes may be associated due to a third confounding variable or chance.
A. A is false but R is true
B. A is true but R is false
C. Both A and R are true, but R is not the correct explanation of A
D. Both A and R are true, and R is the correct explanation of A
Discuss
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Correct Answer: Option D

Explanation:
Statistical association indicates a relationship but not causality; confounding factors or random variation can create spurious associations, necessitating careful interpretation beyond correlation.
This question belongs to: Accountancy and Statistics Statistics
Question #1139
Index numbers are primarily used to:
A. Measure absolute values of economic variables
B. Determine the mode of categorical data
C. Compare relative changes in a variable or group of variables over time or space
D. Calculate the arithmetic mean of a dataset
Discuss
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Correct Answer: Option C

Explanation:
Index numbers express relative changes in a variable (e.g., prices, quantities) compared to a base period or location, facilitating comparison of trends, inflation, or economic performance.
This question belongs to: Accountancy and Statistics Statistics
Question #1140
A fixed base index uses:
A. The immediately preceding period as the base for each calculation
B. A single, constant base period for all comparisons
C. A different base period for each time point
D. Geometric mean of multiple base periods
Discuss
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Correct Answer: Option B

Explanation:
Fixed base index selects one period as the base (index=100) and expresses all other periods relative to it, enabling consistent long-term trend analysis without base drift.
This question belongs to: Accountancy and Statistics Statistics

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