Practice these 17 solved objective-type Statistics MCQs from the 2024 Lahore Board Inter Part 1 (1st Annual) Paper I exam. Each question below includes the verified correct answer and a short explanation to help you understand the concept, not just memorize it. Scroll down to attempt the interactive quiz version with instant scoring.

1. In a discrete probability distribution the sum of all the probabilities is:

(A) 0   (B) 1   (C) -1   (D) ∞

Correct Answer: (B) 1 — The probabilities of all possible outcomes in a discrete distribution must always add up to 1.

2. The standard deviation is always computed from:

(A) Mean   (B) Median   (C) Mode   (D) G.M

Correct Answer: (A) Mean — Standard deviation measures the average squared deviation of values from the mean.

3. Which one is correct:

(A) G.M > H.M   (B) H.M > G.M   (C) H.M > A.M   (D) G.M > A.M

Correct Answer: (A) G.M > H.M — For any data set, A.M ≥ G.M ≥ H.M always holds, so G.M is greater than H.M.

4. When 'r' objects chosen from 'n' objects without regard of order is called:

(A) Permutation   (B) Combination   (C) Factorial   (D) Multiplication

Correct Answer: (B) Combination — When order doesn't matter in a selection, it is called a combination.

5. The price index P₀ₙ = Σpₙqₙ / Σp₀qₙ × 100 is:

(A) Value index   (B) Fisher's index   (C) Laspeyre's index   (D) Paasche's index

Correct Answer: (D) Paasche's index — Using current-period quantities (qₙ) as weights is exactly the definition of Paasche's price index.

6. A numerical characteristic of a sample is called:

(A) Statistic   (B) Parameter   (C) Variable   (D) Population

Correct Answer: (A) Statistic — A numerical value computed from sample data (not the whole population) is a statistic.

7. In a hypergeometric distribution N = 6, n = 2, K = 3 then the mean is:

(A) 2   (B) 3   (C) 1   (D) 4

Correct Answer: (C) 1 — Mean = nK/N = (2 × 3)/6 = 1.

8. If Σ(X − 20) = 25 and Σ(X − 18) = 0, then arithmetic mean is:

(A) 20   (B) 18   (C) 25   (D) Zero

Correct Answer: (B) 18 — Σ(X − A) = 0 exactly when A equals the mean, so the mean is 18.

9. If P(A ∩ B) = 0 then events 'A' and 'B' are called:

(A) Mutually exclusive   (B) Exhaustive   (C) Independent   (D) Dependent

Correct Answer: (A) Mutually exclusive — Events that can never occur together have an intersection probability of zero, making them mutually exclusive.

10. Life of a T.V. tube is a:

(A) Discrete variable   (B) Continuous variable   (C) Qualitative variable   (D) Constant

Correct Answer: (B) Continuous variable — Lifespan can take any value within a range (e.g. hours, days), making it continuous.

11. If P₀₁ (Laspeyre's) = 110, P₀₁ (Paasche's) = 120 then P₀₁ (Fisher's) is:

(A) 110   (B) 120   (C) Zero   (D) 114.89

Correct Answer: (D) 114.89 — Fisher's index is the geometric mean of Laspeyre's and Paasche's: √(110 × 120) ≈ 114.89.

12. Classification of data according to locations or areas is called ___ classification:

(A) Temporal   (B) Qualitative   (C) Geographical   (D) Quantitative

Correct Answer: (C) Geographical — Grouping data by location or region is geographical classification.

13. For a binomial distribution p = q = 1/2 then the distribution is:

(A) Symmetrical   (B) Positively skewed   (C) Negatively skewed   (D) Not exists

Correct Answer: (A) Symmetrical — When p = q = 1/2, the binomial distribution is perfectly balanced and hence symmetrical.

14. A number assigned to outcome of a random experiment is called:

(A) Random number   (B) Random variable   (C) Constant   (D) Sample space

Correct Answer: (B) Random variable — A random variable assigns a numerical value to each outcome of a random experiment.

15. The parameters of hypergeometric distribution are:

(A) n, N   (B) n, K   (C) N, K   (D) n, N, K

Correct Answer: (D) n, N, K — A hypergeometric distribution is defined by sample size n, population size N, and number of successes K.

16. Mean deviation for data 5, 5, 5 is:

(A) 5   (B) 25   (C) Zero   (D) Negative

Correct Answer: (C) Zero — All values are identical, so there is no deviation from the mean at all.

17. An ogive is a:

(A) Frequency curve   (B) Frequency polygon   (C) Histogram   (D) Cumulative frequency polygon

Correct Answer: (D) Cumulative frequency polygon — An ogive is the graph of a cumulative frequency distribution.

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