Practice these 17 solved objective-type Statistics MCQs from the 2022 Lahore Board Inter Part 1 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. If X = a, then X̄ is equal to:
(A) x (B) 0 (C) a (D) 1
Correct Answer: (C) a — If every value equals the constant a, the mean is also a.
2. First moment about mean is always equal to:
(A) 1 (B) -1 (C) 2 (D) Zero
Correct Answer: (D) Zero — Deviations from the mean always cancel out to zero.
3. If X is a random variable, then V(X) is:
(A) E[X−E(X)] (B) E[X−E(X)]² (C) E(X²)−[E(X)]² (D) Both B and C
Correct Answer: (D) Both B and C — Variance can be written either way; both formulas give the same result.
4. In a binomial distribution, the successive trails are:
(A) Independent (B) Dependent (C) Mutually exclusive (D) Fixed
Correct Answer: (A) Independent — Each trial in a binomial distribution doesn't affect the others.
5. Qualities which do not vary:
(A) Variables (B) Constants (C) Statistic (D) All
Correct Answer: (B) Constants — A quantity that keeps the same value throughout is a constant.
6. Probability of sample space is equal to:
(A) Zero (B) 1 (C) -1 (D) 2
Correct Answer: (B) 1 — The sample space covers all possible outcomes, so its probability is 1.
7. The number of values falling in a particular category is called:
(A) Tally mark (B) Class (C) Frequency (D) Class mark
Correct Answer: (C) Frequency — This count is exactly what frequency means.
8. In chain base method, the base period is:
(A) Fixed (B) Constant (C) Changed (D) None
Correct Answer: (C) Changed — The base period shifts to the immediately preceding period each time.
9. Binomial distribution is negatively skewed if:
(A) p < q (B) p > q (C) p = q (D) p = 0.5
Correct Answer: (B) p > q — A higher success probability pulls the tail to the left, making it negatively skewed.
10. If a distribution is mesokurtic, then:
(A) β₂ = 3 (B) β₂ < 3 (C) β₂ > 3 (D) β₁ ≠ 3
Correct Answer: (A) β₂ = 3 — Mesokurtic distributions have the same peakedness as the normal curve.
11. Total angles of a pie chart are:
(A) 360° (B) 180° (C) 190° (D) 90°
Correct Answer: (A) 360° — A pie chart is a full circle, which always spans 360°.
12. If Σ(X − X̄)² = 232 and n = 9, then m₂ is:
(A) 24.78 (B) 25.78 (C) 26.78 (D) 27.78
Correct Answer: (B) 25.78 — m₂ = Σ(X−X̄)²/n = 232/9 ≈ 25.78.
13. Geometric mean of 2 and 8 is:
(A) 8 (B) 4 (C) 5 (D) 2
Correct Answer: (B) 4 — GM = √(2 × 8) = √16 = 4.
14. The index given by Σpₙqₙ / Σp₀qₙ is:
(A) Laspeyre's index (B) Paasche's index (C) Value index (D) Fisher's index
Correct Answer: (B) Paasche's index — Weighting by current-period quantities (qₙ) in both numerator and denominator defines Paasche's index.
15. If ΣX = 400 and X̄ = 25, then n is:
(A) 12 (B) 14 (C) 18 (D) 16
Correct Answer: (D) 16 — n = ΣX/X̄ = 400/25 = 16.
16. Which of the following cannot be the probability of an event:
(A) 1.75 (B) Zero (C) 0.36 (D) 0.82
Correct Answer: (A) 1.75 — Probability must lie between 0 and 1, so 1.75 is invalid.
17. E[X − E(X)] is equal to:
(A) Variance (B) Standard deviation (C) Mean (D) Zero
Correct Answer: (D) Zero — E[X − E(X)] = E(X) − E(X) = 0.
Now try the interactive version of this quiz below to test your score instantly:
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