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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Page 44 of 66
Question #861
Which of the following measures of central tendency is based on all observations and is most affected by extreme values?
A. Median
B. Arithmetic mean
C. Harmonic mean
D. Mode
Discuss
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Correct Answer: Option B

Explanation:
Arithmetic mean uses every value and is pulled towards outliers.
This question belongs to: Accountancy and Statistics Statistics
Question #862
Assertion (A): The arithmetic mean of a set of positive numbers is always greater than or equal to the geometric mean. Reason (R): AM ≥ GM for any set of non-negative numbers, and equality holds when all numbers are equal. Choose the correct option:
A. A is true, R is false
B. A is false, R is true
C. Both A and R are true, and R is the correct explanation of A
D. Both A and R are true, but R is not the correct explanation of A
Discuss
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Correct Answer: Option C

Explanation:
AM-GM inequality is a fundamental property. R correctly states the condition and explains A.
This question belongs to: Accountancy and Statistics Statistics
Question #863
If the geometric mean of a set of numbers is zero, which statement must be true?
A. At least one number is zero.
B. All numbers are negative.
C. All numbers are zero.
D. All numbers are equal.
Discuss
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Correct Answer: Option A

Explanation:
Geometric mean becomes zero if any observation is zero.
This question belongs to: Accountancy and Statistics Statistics
Question #864
For a positive dataset, if the harmonic mean is equal to the arithmetic mean, what can be concluded?
A. The data are symmetric
B. The median equals the mode
C. There is one outlier
D. All values are equal
Discuss
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Correct Answer: Option D

Explanation:
For positive numbers, AM = GM = HM only when all values are identical.
This question belongs to: Accountancy and Statistics Statistics
Question #865
Consider the following statements: 1. Weighted mean considers the relative importance of different items. 2. Combined mean depends on group sizes and group means. 3. Arithmetic mean is always the best measure for skewed data. Which is/are correct?
A. 1 and 3 only
B. 2 and 3 only
C. 1, 2 and 3
D. 1 and 2 only
Discuss
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Correct Answer: Option D

Explanation:
Statement 3 is false because median is preferred for skewed data. 1 and 2 are true.
This question belongs to: Accountancy and Statistics Statistics
Question #866
Assertion (A): For a moderately skewed distribution, mean – mode ≈ 3(mean – median). Reason (R): In any skewed distribution, the median always lies between the mean and mode. Choose the correct option:
A. A is true, R is false
B. A is false, R is true
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 C

Explanation:
The empirical relationship (A) is true for moderate skewness. In skewed distributions, median lies between mean and mode, but this fact does not directly explain the formula; it's an observed pattern.
This question belongs to: Accountancy and Statistics Statistics
Question #867
Which measure of central tendency minimizes the sum of absolute deviations?
A. Median
B. Arithmetic mean
C. Geometric mean
D. Mode
Discuss
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Correct Answer: Option A

Explanation:
Median minimizes Σ|x - M|, while mean minimizes Σ(x - μ)².
This question belongs to: Accountancy and Statistics Statistics
Question #868
If the arithmetic mean of 10 numbers is 40 and the mean of the same numbers after subtracting a constant from each is 25, the constant subtracted was:
A. 20
B. 15
C. 25
D. 10
Discuss
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Correct Answer: Option B

Explanation:
New mean = old mean - constant ⇒ 25 = 40 - k ⇒ k = 15.
This question belongs to: Accountancy and Statistics Statistics
Question #869
A set of values has mean 20. If each value is multiplied by 2 and then 5 is added, the new mean is:
A. 45
B. 50
C. 40
D. 25
Discuss
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Correct Answer: Option A

Explanation:
New mean = 2 × 20 + 5 = 45.
This question belongs to: Accountancy and Statistics Statistics
Question #870
In a classroom, the average weight of 20 boys is 60 kg and that of 30 girls is 50 kg. The combined average weight of all students is:
A. 54 kg
B. 55 kg
C. 52 kg
D. 53 kg
Discuss
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Correct Answer: Option A

Explanation:
Combined mean = (20×60 + 30×50) / 50 = (1200+1500)/50 = 2700/50 = 54 kg.
This question belongs to: Accountancy and Statistics Statistics
Question #871
Which of the following averages cannot be calculated if a dataset contains a zero?
A. Arithmetic mean
B. Harmonic mean
C. Geometric mean
D. Median
Discuss
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Correct Answer: Option B

Explanation:
Harmonic mean involves reciprocals, so zero makes it undefined. Geometric mean with zero is zero, but it is defined; arithmetic and median unaffected.
This question belongs to: Accountancy and Statistics Statistics
Question #872
Assertion (A): In any probability distribution, P(A) + P(A') = 1. Reason (R): A and A' are mutually exclusive and exhaustive events. Choose the correct option:
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 false, R is true
D. A is true, R is false
Discuss
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Correct Answer: Option A

Explanation:
Complementary events partition the sample space, so their probabilities sum to 1. R correctly explains A.
This question belongs to: Accountancy and Statistics Statistics
Question #873
Given P(A)=0.7, P(B)=0.5, and P(A∩B)=0.45. Which statement is correct?
A. A and B are dependent, and P(A|B) = 0.9.
B. P(A∪B) = 0.8.
C. A and B are mutually exclusive.
D. A and B are independent.
Discuss
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Correct Answer: Option A

Explanation:
P(A|B)=0.45/0.5=0.9 ≠ P(A)=0.7, so dependent. P(A∪B)=0.7+0.5-0.45=0.75 ≠ 0.8.
This question belongs to: Accountancy and Statistics Statistics
Question #874
Which of the following pairs of events are independent?
A. Drawing two cards without replacement from a deck: A = first is an ace, B = second is an ace.
B. Selecting a student from a class: A = student is male, B = student plays on the football team (all footballers are male).
C. Tossing a fair coin twice: A = first toss is head, B = second toss is tail.
D. Rolling a die twice: A = first roll is 5, B = sum is 10.
Discuss
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Correct Answer: Option C

Explanation:
Coin tosses are independent. In A, without replacement, not independent. In B, outcome of first affects probability of sum. In D, P(B|A) >0 but P(B|A')=0, so not independent.
This question belongs to: Accountancy and Statistics Statistics
Question #875
Assertion (A): If A and B are independent events, then A' and B' are also independent. Reason (R): P(A'∩B') = P(A')P(B') when A and B are independent. Choose the correct option:
A. A is true, R is false
B. Both A and R are true, but R is not the correct explanation of A
C. Both A and R are true, and R is the correct explanation of A
D. A is false, R is true
Discuss
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Correct Answer: Option C

Explanation:
If A and B are independent, then their complements are independent. The formula P(A'∩B') = (1-P(A))(1-P(B)) holds, so R is true and explains A.
This question belongs to: Accountancy and Statistics Statistics
Question #876
In a certain test, 5% of patients have a disease. The test is positive for 90% of diseased and 10% of healthy. If a patient tests positive, the probability they have the disease is about:
A. 0.32
B. 0.10
C. 0.50
D. 0.90
Discuss
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Correct Answer: Option A

Explanation:
P(D)=0.05, P(+|D)=0.9, P(+|D')=0.1. P(D|+) = (0.05×0.9) / (0.05×0.9 + 0.95×0.1) = 0.045/(0.045+0.095)=0.045/0.14≈0.321.
This question belongs to: Accountancy and Statistics Statistics
Question #877
Consider the following statements about probability: 1. For any two events, P(A∪B) ≤ P(A) + P(B). 2. If A ⊆ B, then P(A) ≤ P(B). 3. For independent events, P(A|B) = P(A). Which of the above is/are correct?
A. 1 and 3 only
B. 2 and 3 only
C. 1 and 2 only
D. 1, 2 and 3
Discuss
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Correct Answer: Option D

Explanation:
All are fundamental axioms/theorems of probability.
This question belongs to: Accountancy and Statistics Statistics
Question #878
If P(A) = 0.5, P(B) = 0.3, and P(A∪B) = 0.7, then P(A|B) equals:
A. 0.6
B. 0.2
C. 0.5
D. 0.33
Discuss
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Correct Answer: Option D

Explanation:
P(A∩B)=0.5+0.3-0.7=0.1. P(A|B)=0.1/0.3≈0.333.
This question belongs to: Accountancy and Statistics Statistics
Question #879
For two events, P(A)=0.4, P(B)=0.3, and P(A∩B)=0.12. Which of the following is true?
A. A and B are independent.
B. A and B are mutually exclusive.
C. A and B are complementary.
D. P(A∪B)=0.52.
Discuss
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Correct Answer: Option A

Explanation:
0.4×0.3=0.12, so independent. Mutually exclusive would need 0. P(A∪B)=0.4+0.3-0.12=0.58.
This question belongs to: Accountancy and Statistics Statistics
Question #880
Which of the following statements about attributes is false?
A. Consistency requires all ultimate frequencies to be positive.
B. Yule's Q ranges from -1 to +1.
C. The number of ultimate classes for n attributes is 2^n.
D. Ultimate class frequencies are mutually exclusive and exhaustive.
Discuss
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Correct Answer: Option A

Explanation:
Consistency requires non-negative (≥0), not strictly positive. Some can be zero.
This question belongs to: Accountancy and Statistics Statistics

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