Practice these 17 solved objective-type Statistics MCQs from the 2015 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. The variance of 5, 5, 5, 5 and 5 is:
(A) Zero (B) 25 (C) 5 (D) 125
Correct Answer: (A) Zero — All five values are identical, so there is no spread at all — the variance is zero.
2. If N = 40, n = 5, K = 4, then mean of hypergeometric distribution is:
(A) 1 (B) 1/2 (C) 1/4 (D) 1/3
Correct Answer: (B) 1/2 — Mean = nK/N = (5 × 4)/40 = 20/40 = 1/2.
3. When two dice are rolled, the number of possible outcomes are:
(A) 6 (B) 12 (C) 36 (D) 48
Correct Answer: (C) 36 — Each die has 6 faces, so total outcomes = 6 × 6 = 36.
4. The frequency of a class divided by total frequency is called:
(A) Class frequency (B) Cumulative frequency (C) Relative frequency (D) Total frequency
Correct Answer: (C) Relative frequency — Dividing a class's frequency by the total frequency gives its relative frequency.
5. In a symmetrical distribution Q₁ = 4, Q₃ = 12, then median is:
(A) 4 (B) 6 (C) 8 (D) Zero
Correct Answer: (C) 8 — In a symmetrical distribution, median = (Q₁ + Q₃)/2 = (4 + 12)/2 = 8.
6. For computing chain index number, we compute:
(A) Price relative (B) Link relative (C) Weighted indices (D) None of these
Correct Answer: (B) Link relative — Chain index numbers are built from link relatives, comparing each period to the one right before it.
7. How many methods are used for the collection of data:
(A) 1 (B) 2 (C) 3 (D) 4
Correct Answer: (B) 2 — Data is collected by two methods: primary and secondary.
8. For a binomial distribution, the variance (npq) is:
(A) 0 (B) Greater than zero (C) Less than zero (D) None of these
Correct Answer: (B) Greater than zero — Since 0 < p < 1, the product npq is always positive.
9. If p = q = 1/2, then binomial distribution is called:
(A) Symmetrical (B) Skewed (C) Positively skewed (D) Negative skewed
Correct Answer: (A) Symmetrical — When p = q = 1/2, the binomial distribution is perfectly balanced.
10. Mean is affected by change of:
(A) Origin (B) Scale (C) Both A and B (D) None of these
Correct Answer: (C) Both A and B — The mean shifts with a change of origin and is rescaled with a change of scale.
11. For a random variable X, ΣP(X) is equal to:
(A) Zero (B) 1 (C) Greater than 1 (D) Less than 1
Correct Answer: (B) 1 — The probabilities of all possible values of a random variable must sum to 1.
12. Sum of absolute deviations of the values is least, when deviations are taken from:
(A) Mean (B) Median (C) Mode (D) G.M.
Correct Answer: (B) Median — The sum of absolute deviations is minimized when measured from the median.
13. If A and B are mutually exclusive events, then P (A ∩ B) is:
(A) Zero (B) 1 (C) 0.5 (D) 0.8
Correct Answer: (A) Zero — Mutually exclusive events cannot occur together, so their intersection has probability zero.
14. Smoking habits of residents of a city are:
(A) Qualitative data (B) Quantitative data (C) Discrete data (D) Continuous data
Correct Answer: (A) Qualitative data — A smoking habit describes a quality/attribute, not a measurable number.
15. Which of the following average is most suitable for computing chain index number:
(A) A.M. (B) Median (C) G.M. (D) H.M.
Correct Answer: (C) G.M. — The geometric mean is best suited for chain index numbers since it handles ratios properly.
16. If X and Y are independent variables then E (XY) is equal to:
(A) E(X).E(Y) (B) X E(Y) (C) Y E(X) (D) None of these
Correct Answer: (A) E(X).E(Y) — For independent variables, E(XY) = E(X) × E(Y).
17. If Q₃ = 20, Q₁ = 10, the coefficient of quartile deviation is:
(A) 3 (B) 1/3 (C) 2/3 (D) 1
Correct Answer: (B) 1/3 — Coefficient of QD = (Q₃ − Q₁)/(Q₃ + Q₁) = (20 − 10)/(20 + 10) = 10/30 = 1/3.
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