Practice these 17 solved objective-type Statistics MCQs from the 2014 Lahore Board Inter Part 1 Paper I exam. Each question below includes the verified correct answer and a short explanation. Scroll down to attempt the interactive quiz version with instant scoring.
1. The observation which occurs maximum number of times is called:
(A) Mean (B) Median (C) Mode (D) H.M.
Correct Answer: (C) Mode — The value that occurs most frequently in a data set is, by definition, the mode.
2. A discrete probability function f(x) is always:
(A) Non-negative (B) Negative (C) One (D) Zero
Correct Answer: (A) Non-negative — Probabilities can never be negative.
3. Coefficient of Quartile Deviation is:
(A) (Q₃ − Q₁) / (Q₃ + Q₁) (B) (Q₃ + Q₁) / (Q₃ − Q₁) (C) (Q₁ + Q₃) / (Q₁ − Q₃) (D) (Q₁ − Q₃) / (Q₁ + Q₃)
Correct Answer: (A) (Q₃ − Q₁) / (Q₃ + Q₁) — This is the standard formula for the coefficient of quartile deviation.
4. Two events A & B are mutually exclusive if:
(A) A ∪ B = φ (B) A ∩ B = φ (C) A ∩ B = S (D) A ∩ B = 1
Correct Answer: (B) A ∩ B = φ — Mutually exclusive events share no common outcomes, so their intersection is empty.
5. The branch of Statistics which deals with procedures of drawing inferences about the population on the basis of sample information is called:
(A) Descriptive Statistics (B) Inferential Statistics (C) Applied Statistics (D) Theoretical Statistics
Correct Answer: (B) Inferential Statistics — Drawing conclusions about a population from sample data is exactly what inferential statistics does.
6. If all the values are not of equal importance, the index number is called:
(A) Weighted (B) Unweighted (C) Simple (D) None of these
Correct Answer: (A) Weighted — When items are given different importance in an index, it's called a weighted index number.
7. In a hypergeometric experiment, the probability of each outcome ___ from trial to trial:
(A) Remains constant (B) Changes (C) Depends on N (D) Depends on n
Correct Answer: (B) Changes — Since sampling is without replacement, the probability of each outcome changes from trial to trial.
8. The total area under the curve of a continuous probability density function is always equal to:
(A) 0 (B) 1 (C) −1 (D) ∞
Correct Answer: (B) 1 — By definition, the total area under any probability density function always equals 1.
9. For binomial distribution:
(A) Mean < Variance (B) Mean > Variance (C) Mean ≤ Variance (D) Mean = Variance
Correct Answer: (B) Mean > Variance — Since Variance = npq and Mean = np, and q < 1, the mean is always greater than the variance.
10. In a percentage frequency distribution the total of percentage frequencies is:
(A) 1 (B) 100 (C) Σf (D) Σx
Correct Answer: (B) 100 — Percentage frequencies always add up to 100.
11. For symmetric distributions:
(A) Mean < Median < Mode (B) Mean > Median > Mode (C) Mean < Mode < Median (D) Mean = Median = Mode
Correct Answer: (D) Mean = Median = Mode — In a perfectly symmetric distribution, all three coincide at the same value.
12. The binomial distribution has ___ parameters:
(A) 0 (B) 1 (C) 2 (D) 3
Correct Answer: (C) 2 — The binomial distribution is defined by two parameters: n and p.
13. The general purchasing power of the currency of a country is determined by:
(A) Retail price index (B) Volume index (C) Composite index (D) Wholesale price index
Correct Answer: (D) Wholesale price index — It tracks broad price changes and is used to gauge a currency's purchasing power.
14. If A is an empty set and S is the sample space then:
(A) P(A ∪ S) = 1 (B) P(A ∩ S) = 1 (C) P(A ∪ S) = 0 (D) P(A) = P(S)
Correct Answer: (A) P(A ∪ S) = 1 — Since A is empty, A ∪ S = S, and P(S) is always 1.
15. Arithmetic mean for X₁ and X₂:
(A) 2 / (X₁ + X₂) (B) 2X₁X₂ / (X₁ + X₂) (C) (X₁ + X₂) / 2 (D) √(X₁X₂)
Correct Answer: (C) (X₁ + X₂) / 2 — The arithmetic mean of two values is their sum divided by 2.
16. The value of standard deviation changes by a change of:
(A) Origin (B) Scale (C) Algebraic sign (D) Both A and B
Correct Answer: (B) Scale — S.D. is unaffected by shifting the origin, but is rescaled by a change of scale.
17. Suitable average for averaging to shoe sizes is:
(A) Mean (B) Median (C) Mode (D) Geometric mean
Correct Answer: (C) Mode — Shoe sizes need the most commonly occurring value rather than an arithmetic average.
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