Practice these 17 solved objective-type Statistics MCQs from the 2016 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. A quantity calculated from the sample is called:
(A) Statistic (B) Sample (C) Parameter (D) None of these
Correct Answer: (A) Statistic — A numerical value computed from sample data is called a statistic.
2. The grouped data is:
(A) Primary data (B) Secondary data (C) Raw data (D) None of these
Correct Answer: (B) Secondary data — Once raw (primary) data is classified into groups, it has already been processed, making it secondary data.
3. The graphic representation of the frequency distribution is:
(A) Frequency curve (B) Historigram (C) Ogive (D) Histogram
Correct Answer: (D) Histogram — A frequency distribution is graphically represented by a histogram.
4. If Σ(x − 20) = 25, Σ(x − 15) = 0 and Σ(x − 10) = −10 then arithmetic mean is:
(A) 25 (B) −10 (C) 15 (D) 20
Correct Answer: (C) 15 — Σ(x − A) = 0 exactly when A equals the mean, so since Σ(x − 15) = 0, the mean is 15.
5. Geometric mean of 2, 4, 8 is:
(A) Zero (B) 16 (C) 8 (D) 4
Correct Answer: (D) 4 — GM = ³√(2 × 4 × 8) = ³√64 = 4.
6. Second moment about mean is:
(A) Variance (B) Standard deviation (C) Zero (D) One
Correct Answer: (A) Variance — By definition, the second central moment (moment about the mean) is the variance.
7. In a symmetrical distribution, the coefficient of skewness will always be:
(A) Negative (B) Zero (C) 1 (D) −1
Correct Answer: (B) Zero — A symmetrical distribution has no skew in either direction.
8. If β₂ = 3 then the distribution is called:
(A) Symmetrical (B) Mesokurtic (C) Platykurtic (D) Leptokurtic
Correct Answer: (B) Mesokurtic — β₂ = 3 matches the kurtosis of the normal curve, so it's called mesokurtic.
9. Index number for the base period is always taken as:
(A) One (B) Zero (C) 100 (D) 200
Correct Answer: (C) 100 — By convention, the base period index number is always fixed at 100.
10. Laspeyre's index number is:
(A) Σp₀q₀ / Σpₙq₀ (B) Σpₙq₀ / Σp₀q₀ (C) Σpₙqₙ / Σp₀q₀ (D) Σpₙqₙ / Σpₙqₙ
Correct Answer: (B) Σpₙq₀ / Σp₀q₀ — Laspeyre's index uses base-period quantities as weights: Σpₙq₀ / Σp₀q₀ (×100).
11. The probability of an event cannot be:
(A) Zero (B) Greater than zero (C) One (D) Less than zero
Correct Answer: (D) Less than zero — Probability always lies between 0 and 1, so it can never be negative.
12. The probability of selecting a red card out of 52 playing cards is:
(A) 13/52 (B) 4/52 (C) 1/52 (D) 26/52
Correct Answer: (D) 26/52 — 26 of the 52 cards are red (hearts and diamonds).
13. In a discrete probability distribution, the sum of all the probabilities is always equal to:
(A) Minimum (B) Maximum (C) Zero (D) One
Correct Answer: (D) One — The probabilities of all possible outcomes must add up to one.
14. E (X + 2Y) is equal to:
(A) E(X) + 2E(Y) (B) E(X) + 4E(Y) (C) E(2X) + E(2Y) (D) E(X) + E(Y)
Correct Answer: (A) E(X) + 2E(Y) — By linearity of expectation, E(X + 2Y) = E(X) + 2E(Y).
15. In a binomial distribution p = q = 1/2, then the distribution is:
(A) Symmetrical (B) Positively skewed (C) Negatively skewed (D) Biased
Correct Answer: (A) Symmetrical — When p = q = 1/2, the binomial distribution is perfectly balanced.
16. The parameters of the hypergeometric distribution are:
(A) n, p, q (B) n, N, p (C) n, N, k (D) n, N, q
Correct Answer: (C) n, N, k — Defined by population size N, sample size n, and number of successes k.
17. The hypergeometric probability distribution is:
(A) Continuous distribution (B) Simple distribution (C) Discrete distribution (D) None of these
Correct Answer: (C) Discrete distribution — It models counts of successes without replacement, making it discrete.
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