Practice these 17 solved objective-type Statistics MCQs from the 2012 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. If the Mean = 40, Mode = 42, the distribution is:
(A) Symmetrical (B) +vely skewed (C) −vely skewed (D) None of these
Correct Answer: (C) −vely skewed — Since Mode (42) > Mean (40), the longer tail is on the left, making it negatively skewed.
2. If X and Y are two independent variable then E (XY) =
(A) E(X) + E(Y) (B) E(X).E(Y) (C) E(X) − E(Y) (D) Zero
Correct Answer: (B) E(X).E(Y) — For independent variables, E(XY) = E(X) × E(Y).
3. Standard deviation of 3, 3, 3, 3, 3 is equal to:
(A) 8 (B) 3 (C) Zero (D) 16
Correct Answer: (C) Zero — All values are identical, so there is no spread at all.
4. The number of permutation for 'r' objects taken out of total 'n' objects is:
(A) ⁿCₙ (B) ⁿCᵣ (C) ⁿPᵣ (D) ⁿCᵣ
Correct Answer: (C) ⁿPᵣ — Arranging r objects chosen from n, where order matters, is given by the permutation formula ⁿPᵣ.
5. Colour of hair is a:
(A) Continuous variable (B) Discrete variable (C) Qualitative variable (D) Quantitative variable
Correct Answer: (C) Qualitative variable — Hair colour describes a quality/attribute rather than a measurable number.
6. If all the values consider equal importance in index number is:
(A) Simple (B) Weighted (C) Unweighted (D) None of these
Correct Answer: (C) Unweighted — When every item is given equal importance, the index number is called unweighted.
7. Mean of binomial distribution is:
(A) npq (B) xp (C) np (D) √npq
Correct Answer: (C) np — For a binomial distribution, the mean is np.
8. An expected value of a random variable is equal to its:
(A) Variance (B) Mean (C) S.D. (D) None of these
Correct Answer: (B) Mean — The expected value of a random variable is, by definition, its mean.
9. The hypergeometric distribution has parameters:
(A) 2 (B) 3 (C) 4 (D) None of these
Correct Answer: (B) 3 — Defined by population size N, sample size n, and number of successes k.
10. An ogive is a:
(A) Frequency polygon (B) Frequency curve (C) Cumulative frequency (D) None of these
Correct Answer: (C) Cumulative frequency — An ogive is the graph of a cumulative frequency distribution.
11. First moment about mean is equal to:
(A) One (B) 3 (C) Zero (D) All of these
Correct Answer: (C) Zero — The first central moment is always zero.
12. In a binomial experiment, the successive trials are:
(A) Independent (B) Fixed (C) Dependent (D) Mutually
Correct Answer: (A) Independent — Each trial in a binomial experiment is independent of the others.
13. The index number given by Σpₙq₀ / Σp₀q₀ × 100 is:
(A) Laspeyre's index (B) Value index (C) Paasche's index (D) None of these
Correct Answer: (A) Laspeyre's index — Using fixed base-period quantities (q₀) as weights defines Laspeyre's index.
14. The probability of sure event is:
(A) Negative (B) Zero (C) One (D) None of these
Correct Answer: (C) One — A sure event is guaranteed to happen, so its probability is always 1.
15. The sum of deviation from mean is:
(A) 5 (B) Zero (C) 3 (D) 1
Correct Answer: (B) Zero — Deviations from the mean always cancel out to zero.
16. The difference between largest and smallest value is:
(A) Interval (B) S.D. (C) Range (D) None of these
Correct Answer: (C) Range — The range is defined as the difference between the largest and smallest values.
17. What is total angle of pie diagram:
(A) 90° (B) 180° (C) 360° (D) None of these
Correct Answer: (C) 360° — A pie diagram is a full circle, which always spans 360°.
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