Practice these 17 solved objective-type Statistics MCQs from the 2011 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. Registration is the source of:
(A) Primary data (B) Secondary data (C) Variable (D) Information
Correct Answer: (B) Secondary data — Registration records (like birth/death registers) are existing records collected for another purpose, making them secondary data.
2. Mid points of top of the rectangular of histogram are joined to get:
(A) Frequency polygon (B) Frequency curve (C) Ogive (D) Histogram
Correct Answer: (A) Frequency polygon — Joining the midpoints of histogram bar tops produces a frequency polygon.
3. Given classes: 1 – 5, 6 – 10, - - - - - class interval size is:
(A) 5.5 (B) 3 (C) 4 (D) 5
Correct Answer: (D) 5 — Class interval size is found from the difference between successive lower limits: 6 − 1 = 5.
4. Geometric mean of X: 2, 4, 8 is:
(A) Zero (B) 4 (C) 6 (D) 16
Correct Answer: (B) 4 — GM = ³√(2 × 4 × 8) = ³√64 = 4.
5. It is the reciprocal of the simple average of the reciprocal of all the values:
(A) Arithmetic mean (B) G.M. (C) H.M. (D) Mode
Correct Answer: (C) H.M. — This is exactly the definition of the harmonic mean.
6. The mean deviation is least if deviations are taken from:
(A) Median (B) Arithmetic mean (C) Mode (D) G.M.
Correct Answer: (A) Median — Mean deviation is minimized when measured from the median.
7. If S.D of X is 5 then S.D. (2X + 5) / 2 is equal to:
(A) 5 (B) 7.5 (C) 10 (D) 15
Correct Answer: (A) 5 — (2X + 5)/2 simplifies to X + 2.5, just a shift of X, so S.D. stays 5.
8. For Leptokurtic distribution:
(A) β₂ > 3 (B) β₂ < 3 (C) β₂ = 3 (D) β₁ > 3
Correct Answer: (A) β₂ > 3 — A leptokurtic distribution is more peaked than normal, corresponding to β₂ > 3.
9. Link Relative is equal to:
(A) Pₙ / P₀ × 100 (B) Pₙ / Pₙ₋₁ × 100 (C) P₀ / Pₙ × 100 (D) Pₐ / Pₙ × 100
Correct Answer: (B) Pₙ / Pₙ₋₁ × 100 — A link relative compares the current period's price to the immediately preceding period.
10. In price index number, weights are:
(A) Prices (B) Quantities (C) Average price (D) Average quantities
Correct Answer: (B) Quantities — Price index numbers use quantities as weights to combine price relatives.
11. The probability of drawing two aces with replacement from 52 playing cards is:
(A) 1/221 (B) 1/4 (C) 1/16 (D) 1/169
Correct Answer: (D) 1/169 — With replacement, P = (4/52) × (4/52) = (1/13)² = 1/169.
12. A coin and a die can throw together in:
(A) 2 ways (B) 8 ways (C) 4 ways (D) 12 ways
Correct Answer: (D) 12 ways — 2 coin outcomes × 6 die outcomes = 12 total outcomes.
13. A random variable is also called:
(A) Chance variable (B) Independent variable (C) Only discrete variable (D) Only continuous variable
Correct Answer: (A) Chance variable — Since its value depends on a random experiment's outcome, it's also called a chance variable.
14. A distribution function F(X) is equal to:
(A) P(X = x) (B) P(X ≥ x) (C) P(X ≤ x) (D) P(a ≤ x ≤ b)
Correct Answer: (C) P(X ≤ x) — The distribution function is defined as F(x) = P(X ≤ x).
15. Binomial distribution is positive skewed when:
(A) P = q (B) P > q (C) P < q (D) P = 1/2
Correct Answer: (C) P < q — When success is less likely than failure, the distribution's longer tail sits to the right, making it positively skewed.
16. Probability of drawing one white and one black ball from a bag containing 5 white and 4 black ball is:
(A) 4/9 (B) 5/9 (C) 1/9 (D) 9/9
Correct Answer: (B) 5/9 — P = (5C1 × 4C1) / 9C2 = 20/36 = 5/9.
17. In hypergeometric distribution successive trials are:
(A) Independent (B) Large (C) Not fixed (D) Not independent
Correct Answer: (D) Not independent — Since sampling is without replacement, each trial affects the next.
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