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 19 of 66
Question #361
A frequency distribution has classes 0-10, 10-20, 20-30, 30-40. The median class is 20-30 and the cumulative frequency before this class is 30. If N=80, frequency of median class is 20. The median is:
A. 26
B. 25
C. 23
D. 24
Discuss
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Correct Answer: Option B

Explanation:
Median = L + (N/2 - cf)/f × h = 20 + (40-30)/20 × 10 = 20 + 10/20×10 = 20 + 5 = 25.
This question belongs to: Accountancy and Statistics Statistics
Question #362
In a distribution, the mode is 30, median 32, mean 34. The distribution is:
A. Symmetric
B. Negatively skewed
C. Positively skewed
D. Leptokurtic
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Correct Answer: Option C

Explanation:
Mean > Median > Mode indicates positive skewness.
This question belongs to: Accountancy and Statistics Statistics
Question #363
For a symmetric distribution, which statement is correct?
A. Mean = Median = Mode
B. Mode = 3Median - 2Mean
C. Mean - Mode = 3(Mean - Median)
D. Median = (Mean + Mode)/2
Discuss
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Correct Answer: Option A

Explanation:
In a perfectly symmetric distribution, all three central measures coincide.
This question belongs to: Accountancy and Statistics Statistics
Question #364
In a set of 10 numbers, the mean of the first 6 is 15 and the mean of the remaining 4 is 20. The combined mean is:
A. 17
B. 16.5
C. 17.5
D. 18
Discuss
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Correct Answer: Option A

Explanation:
Sum = 6×15 + 4×20 = 90+80=170. Combined mean = 170/10 = 17.
This question belongs to: Accountancy and Statistics Statistics
Question #365
Which measure of central tendency is undefined for data containing zero?
A. Median
B. Geometric mean
C. Harmonic mean
D. Arithmetic mean
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Correct Answer: Option C

Explanation:
Harmonic mean involves reciprocals; if any value is zero, reciprocal is infinite, so it's undefined.
This question belongs to: Accountancy and Statistics Statistics
Question #366
The sample space for tossing two coins simultaneously is:
A. {0,1,2}
B. {HH,HT,TH,TT}
C. {HH,HT,TT}
D. {H,T}
Discuss
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Correct Answer: Option B

Explanation:
Two independent outcomes for each coin yield four ordered pairs.
This question belongs to: Accountancy and Statistics Statistics
Question #367
If P(A)=0.35, P(B)=0.55, and P(A∩B)=0.20, then P(A'∩B') is:
A. 0.30
B. 0.80
C. 0.10
D. 0.70
Discuss
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Correct Answer: Option A

Explanation:
P(A∪B)=0.35+0.55-0.20=0.70. P(A'∩B') = 1 - 0.70 = 0.30.
This question belongs to: Accountancy and Statistics Statistics
Question #368
A speaks truth in 70% cases, B in 80% cases. In what percentage of cases are they likely to contradict each other in stating the same fact?
A. 44%
B. 56%
C. 38%
D. 50%
Discuss
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Correct Answer: Option C

Explanation:
Contradiction = P(A truth and B lie) + P(A lie and B truth) = 0.7×0.2 + 0.3×0.8 = 0.14+0.24=0.38=38%.
This question belongs to: Accountancy and Statistics Statistics
Question #369
Three students A,B,C solve a problem. Probabilities 1/2, 2/3, 3/4. Probability that exactly two of them solve it is:
A. 13/24
B. 7/24
C. 11/24
D. 1/4
Discuss
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Correct Answer: Option C

Explanation:
P(AB'C) = 1/2 * 1/3 * 3/4 = 3/24; P(AB'C)? Let's compute exactly two: A and B not C: 1/2*2/3*1/4=2/24; A not B C: 1/2*1/3*3/4=3/24; not A B C: 1/2*2/3*3/4=6/24. Sum = 11/24.
This question belongs to: Accountancy and Statistics Statistics
Question #370
A card is drawn from a well-shuffled deck of 52 cards. The probability that it is a jack or a spade is:
A. 1/4
B. 4/13
C. 16/52
D. 17/52
Discuss
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Correct Answer: Option C

Explanation:
P(jack)=4/52, spade=13/52, jack of spades=1/52. P=4/52+13/52-1/52=16/52.
This question belongs to: Accountancy and Statistics Statistics
Question #371
A bag contains 5 red, 4 blue, 3 green balls. Two balls are drawn without replacement. Probability that both are same color is:
A. 19/66
B. 12/66
C. 20/66
D. 15/66
Discuss
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Correct Answer: Option A

Explanation:
Total ways C(12,2)=66. Favorable: C(5,2)+C(4,2)+C(3,2) = 10+6+3=19. Probability=19/66.
This question belongs to: Accountancy and Statistics Statistics
Question #372
If P(A)=0.4, P(A∪B)=0.7, then the probability of B will be maximum when A and B are:
A. Mutually exclusive
B. A is a subset of B
C. Independent
D. B is a subset of A
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Correct Answer: Option B

Explanation:
P(A∪B)=P(A)+P(B)-P(A∩B). To maximize P(B) given P(A∪B)=0.7 and P(A)=0.4, set P(A∩B)=P(A)=0.4 (i.e., A⊂B). Then 0.7=0.4+P(B)-0.4 => P(B)=0.7 max.
This question belongs to: Accountancy and Statistics Statistics
Question #373
For independent events A and B with P(A)=0.3, P(B)=0.4, the probability that at least one of them occurs is:
A. 0.82
B. 0.70
C. 0.12
D. 0.58
Discuss
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Correct Answer: Option D

Explanation:
P(A∪B)=0.3+0.4-0.3×0.4=0.7-0.12=0.58.
This question belongs to: Accountancy and Statistics Statistics
Question #374
Given P(A)=0.5, P(B)=0.3, P(A∩B)=0.1. Are A and B independent?
A. Cannot determine
B. Yes, because P(A∩B)=P(A)P(B)
C. Yes, because they are mutually exclusive
D. No, because 0.1 ≠ 0.15
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Correct Answer: Option D

Explanation:
P(A)P(B)=0.5×0.3=0.15 ≠ 0.1, so not independent.
This question belongs to: Accountancy and Statistics Statistics
Question #375
A fair coin is tossed until a head appears. The probability that it takes exactly 3 tosses is:
A. 1/8
B. 1/2
C. 1/4
D. 3/8
Discuss
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Correct Answer: Option A

Explanation:
Sequence: T, T, H. Probability = (1/2)² * (1/2) = 1/8.
This question belongs to: Accountancy and Statistics Statistics
Question #376
A box contains 3 defective and 7 non-defective items. Two items are selected at random. The probability that exactly one is defective is:
A. 1/5
B. 7/15
C. 14/45
D. 21/45
Discuss
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Correct Answer: Option B

Explanation:
Total C(10,2)=45. Favorable: 3×7=21. Probability=21/45=7/15.
This question belongs to: Accountancy and Statistics Statistics
Question #377
If P(A|B) = 0.4 and P(B) = 0.5, P(A∩B) is:
A. 0.8
B. 0.4
C. 0.9
D. 0.2
Discuss
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Correct Answer: Option D

Explanation:
P(A∩B) = P(A|B) P(B) = 0.4 × 0.5 = 0.2.
This question belongs to: Accountancy and Statistics Statistics
Question #378
In Bayes' theorem, the probability P(E_i|A) is called:
A. Posterior probability
B. Prior probability
C. Likelihood
D. Marginal probability
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Correct Answer: Option A

Explanation:
The updated probability after observing the evidence is the posterior probability.
This question belongs to: Accountancy and Statistics Statistics
Question #379
There are two urns: Urn 1 contains 4 white, 6 black; Urn 2 contains 5 white, 5 black. An urn is chosen at random and a ball drawn. If it is white, probability it came from Urn 1 is:
A. 2/5
B. 4/9
C. 1/2
D. 5/9
Discuss
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Correct Answer: Option B

Explanation:
P(Urn1|W) = (1/2 * 4/10) / (1/2*4/10 + 1/2*5/10) = 0.2 / (0.2+0.25)=0.2/0.45=4/9.
This question belongs to: Accountancy and Statistics Statistics
Question #380
In the theory of attributes, the total number of objects N is equal to:
A. (A)+(B)-(AB)
B. (A)+(α)
C. Both A and B
D. (AB)+(Aβ)+(αB)+(αβ)
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Correct Answer: Option C

Explanation:
Both identities hold; (A)+(α)=N, and the sum of ultimate class frequencies also equals N.
This question belongs to: Accountancy and Statistics Statistics

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