Practice these 17 solved objective-type Statistics MCQs from the 2017 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 a and b are two values then geometric mean is:
(A) a × b (B) √(a × b) (C) a + b (D) (a + b) / 2
Correct Answer: (B) √(a × b) — The geometric mean of two values is the square root of their product.
2. A random variable assuming only finite numbers is called:
(A) Continuous (B) Discrete (C) Both A and B (D) None of these
Correct Answer: (B) Discrete — A random variable that can take only a finite (countable) number of values is discrete.
3. Variance of 3, 3, 3, 3 is:
(A) 3 (B) Negative (C) Positive (D) Zero
Correct Answer: (D) Zero — All values are identical, so there is no spread and the variance is zero.
4. The orderly arrangement of units is called:
(A) Permutation (B) Combination (C) Both A and B (D) None of these
Correct Answer: (A) Permutation — An orderly (sequenced) arrangement where order matters is called a permutation.
5. Statistic is a characteristic calculated from:
(A) Population data (B) Sample data (C) Arrayed data (D) Fictitious data
Correct Answer: (B) Sample data — A statistic is, by definition, a numerical characteristic computed from sample data.
6. An index number computed for a single commodity is called:
(A) Simple index (B) Composite index (C) Both A and B (D) None of these
Correct Answer: (A) Simple index — An index number based on just one commodity is called a simple index number.
7. In a hypergeometric distribution N = 6, n = 2, k = 3 then mean is:
(A) 2 (B) 3 (C) 4 (D) 1
Correct Answer: (D) 1 — Mean of a hypergeometric distribution = nk/N = (2 × 3)/6 = 1.
8. If X and Y are two variables then E (X − Y) is:
(A) E(X) − E(Y) (B) E(X) + E(Y) (C) E(X − Y)² (D) E(X + Y)²
Correct Answer: (A) E(X) − E(Y) — By linearity of expectation, E(X − Y) = E(X) − E(Y).
9. If p = q then binomial distribution becomes:
(A) Positive skewed (B) Negative skewed (C) Continuous (D) Symmetrical
Correct Answer: (D) Symmetrical — When p = q (each equal to 1/2), the binomial distribution is perfectly balanced.
10. Cumulative frequency is:
(A) Decreasing (B) Increasing (C) Both A and B (D) Relative frequency
Correct Answer: (B) Increasing — Cumulative frequency keeps adding up as you move through classes, so it always increases.
11. If moment ratio b₁ = 0 then distribution is:
(A) Symmetrical (B) J-shaped (C) U-shaped (D) All of these
Correct Answer: (A) Symmetrical — A zero value of b₁ (skewness) indicates the distribution is symmetrical.
12. If yᵢ = axᵢ + b then var (yᵢ) is:
(A) a var(xᵢ) + b (B) var(xᵢ) (C) a var(xᵢ) (D) a² var(xᵢ)
Correct Answer: (D) a² var(xᵢ) — Variance is unaffected by adding a constant, but scaling by a multiplies variance by a².
13. Price of base period is denoted by:
(A) Pₒₙ (B) Qₒₙ (C) Pₙ (D) Pₒ
Correct Answer: (D) Pₒ — The price in the base period is conventionally denoted P₀.
14. If P(A) = 0.7, P (B) = 0.5, A and B are independent then P(A ∩ B) is:
(A) 1.2 (B) 0.85 (C) 3.5 (D) 0.35
Correct Answer: (D) 0.35 — For independent events, P(A ∩ B) = P(A) × P(B) = 0.7 × 0.5 = 0.35.
15. Mean of first n-natural numbers is:
(A) (n + 1) / 2 (B) n / 2 (C) (n − 1) / 2 (D) n(n + 1) / 2
Correct Answer: (A) (n + 1) / 2 — Their sum n(n+1)/2 divided by n simplifies to (n + 1)/2.
16. A symmetrical distribution has mean = 4 then its mode is:
(A) 4 (B) Less than 4 (C) Greater than 4 (D) Zero
Correct Answer: (A) 4 — In a symmetrical distribution, mean = median = mode, so the mode also equals 4.
17. Pie diagram consists of:
(A) Circle (B) Bars (C) Rectangles (D) All of these
Correct Answer: (A) Circle — A pie diagram represents data as sectors (slices) of a circle.
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