Statistics MCQs 2012 – Lahore Board, Inter Part 2

Practice these 17 solved objective-type Statistics MCQs from the 2012 Lahore Board Inter Part 2, Paper II 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 normal curve is called:

(A) Leptokurtic (B) Platykurtic (C) Mesokurtic (D) Skewed

Correct Answer: (C) Mesokurtic — The standard bell-shaped normal curve has kurtosis β₂ = 3, which is classified as mesokurtic.

2. The area to the left of μ + σ for a normal distribution is approximately equal to:

(A) 0.16 (B) 0.34 (C) 0.50 (D) 0.84

Correct Answer: (D) 0.84 — The area to the left of the mean is 0.5, plus the area between the mean and μ+1σ (≈0.34), giving 0.5 + 0.34 = 0.84.

3. In a normal distribution, the value of β₁ and β₂ are respectively:

(A) 0 and 3 (B) 3 and 0 (C) 0 and 1 (D) 1 and 3

Correct Answer: (A) 0 and 3 — For a normal distribution, the skewness measure β₁ = 0 and the kurtosis measure β₂ = 3.

4. A survey conducted by a sampling design is called:

(A) Population survey (B) Sample survey (C) Systematic survey (D) Pakistan survey

Correct Answer: (B) Sample survey — A survey based on data collected from a sample (selected using a sampling design) is called a sample survey.

5. s² = Σ(x − x̄)² / (n − 1) is called:

(A) Population variance (B) Biased population variance (C) Unbiased sample variance (D) Biased sample variance

Correct Answer: (C) Unbiased sample variance — Dividing the sum of squared deviations by (n − 1) gives the unbiased sample variance.

6. Probability sampling is also called:

(A) Random sampling (B) Non random sampling (C) Biased sampling (D) Judgment sampling

Correct Answer: (A) Random sampling — In probability sampling, every unit has a known chance of selection, which is why it is also called random sampling.

7. θ̂ is called an unbiased estimator of θ if:

(A) E(θ̂) < θ (B) E(θ̂) > θ (C) E(θ̂) ≠ θ (D) E(θ̂) = θ

Correct Answer: (D) E(θ̂) = θ — An estimator is unbiased when its expected value exactly equals the true parameter it is estimating.

8. The confidence interval for μ when σ is known is given by:

(A) X̄ ± z_α/2 × s/√n (B) X̄ ± t_α/2 × σ/√n (C) X̄ ± z_α/2 × σ/√n (D) X̄ ± t_α/2 × s/√n

Correct Answer: (C) X̄ ± z_α/2 × σ/√n — When the population standard deviation σ is known, the confidence interval uses the z-value along with σ.

9. The level of significance is denoted by:

(A) 1 − α (B) α (C) β (D) 1 − β

Correct Answer: (B) α — The level of significance, representing the probability of a Type-I error, is denoted α.

10. When value of b_xy is negative, then b_yx is:

(A) Negative (B) Positive (C) One (D) Zero

Correct Answer: (A) Negative — Both regression coefficients always carry the same sign, so if b_xy is negative, b_yx is also negative.

11. The dependent variable is also called:

(A) Regressor (B) Predictor (C) Predictand (D) Continuous variable

Correct Answer: (C) Predictand — In regression analysis, the dependent (predicted) variable is also called the predictand, while the independent variable is the predictor or regressor.

12. The value of correlation coefficient lies between:

(A) −∞ and +∞ (B) 0 and ∞ (C) −∞ and 0 (D) −1 and +1

Correct Answer: (D) −1 and +1 — The correlation coefficient r always lies within the range −1 to +1, inclusive.

13. The number of cells in a 4 × 3 contingency table are:

(A) 6 (B) 12 (C) 7 (D) 1

Correct Answer: (B) 12 — A contingency table with 4 rows and 3 columns has 4 × 3 = 12 cells.

14. Two attributes A and B are independent if:

(A) (AB) = (A)(B)/n (B) (AB) < (A)(B)/n (C) (AB) > (A)(B)/n (D) (AB) ≠ (A)(B)/n

Correct Answer: (A) (AB) = (A)(B)/n — Two attributes A and B are independent precisely when the observed frequency (AB) equals the expected frequency under independence.

15. The difference between the actual value and the trend value is called:

(A) Slope (B) Residual (C) Intercept (D) Sum of residual

Correct Answer: (B) Residual — The gap between an observed (actual) value and its corresponding trend value is called the residual.

16. Decomposition of time series is called:

(A) Time series (B) Analysis of time series (C) Detrending (D) Deseasonalization

Correct Answer: (B) Analysis of time series — Breaking a time series down into its component parts (trend, seasonal, cyclical, irregular) is called analysis of time series.