Practice these 17 solved objective-type Statistics MCQs from the 2011 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. E(θ̂) − θ is equal to:
(A) Sampling error (B) Non sampling error (C) Bias (D) Standard error
Correct Answer: (C) Bias — The difference between the expected value of an estimator and the true parameter, E(θ̂) − θ, is defined as bias.
2. The mechanical devices that make up the computer are called:
(A) Software (B) Hardware (C) Program (D) AutoCAD
Correct Answer: (B) Hardware — The physical, mechanical and electronic components of a computer are collectively called hardware.
3. The unit of measurement of coefficient of correlation calculated from height (in inches) and weight (in pounds) will be:
(A) Inches (B) Pounds (C) Both inches and pounds (D) As a pure number
Correct Answer: (D) As a pure number — The correlation coefficient is a ratio that cancels out units, so it is always expressed as a pure (unitless) number.
4. In a normal distribution with μ = 0 and σ² = 1 the points of inflection are:
(A) −1 and +1 (B) 0 and +1 (C) −1 and 0 (D) −2 and +2
Correct Answer: (A) −1 and +1 — The points of inflection of a normal curve occur at μ ± σ. Here, that's 0 ± 1.
5. The point estimator of 'μ' is:
(A) p̂ (B) S² (C) X̄ (D) σ
Correct Answer: (C) X̄ — The sample mean X̄ is used as the standard point estimator of the population mean μ.
6. Formula for b_yx is:
(A) S_xy / S²_x (B) S_xy / S²_y (C) S_xy / √S_x² (D) S_xy / √S_y²
Correct Answer: (A) S_xy / S²_x — For the regression of y on x, b_yx is calculated as the covariance divided by the variance of x.
7. The coefficient of skewness of normal distribution is:
(A) −1 (B) 0 (C) +1 (D) +3
Correct Answer: (B) 0 — The normal distribution is perfectly symmetrical, so its coefficient of skewness is 0.
8. Increasing the literacy rate is an example of:
(A) Secular trend (B) Cyclical trend (C) Seasonal trend (D) Irregular trend
Correct Answer: (A) Secular trend — A gradual, long-term increase like rising literacy rate over years reflects the secular trend of a time series.
9. The graph of a time series is called:
(A) Ogive (B) Frequency curve (C) Histogram (D) Historigram
Correct Answer: (D) Historigram — A time series (values plotted against time) is graphically represented as a historigram.
10. Standard error of mean is the standard deviation of:
(A) Population (B) Sample (C) Sampling distribution means (D) Sample design
Correct Answer: (C) Sampling distribution means — The standard error of the mean is defined as the standard deviation of the sampling distribution of the sample mean.
11. The value of Chi-square may be:
(A) −5 (B) −3 (C) −1 (D) Greater than or equal to zero
Correct Answer: (D) Greater than or equal to zero — Since χ² is a sum of squared standardized deviations, its value can never be negative.
12. A value calculated from sample is called:
(A) Parameter (B) Statistic (C) Bias (D) Sampling error
Correct Answer: (B) Statistic — A numerical value computed from sample data (not the whole population) is called a statistic.
13. The regression line of "y on x" is y = −5 + 2x. If x = 5 then value of dependent variable is:
(A) 15 (B) 5 (C) 0 (D) 10
Correct Answer: (B) 5 — Substituting x = 5: y = −5 + 2(5) = −5 + 10 = 5.
14. If X ~ N (55, 100) then area to the right of X = 55 is:
(A) Zero (B) 0.5 (C) 0.75 (D) 1
Correct Answer: (B) 0.5 — Since X = 55 equals the mean, it splits the symmetric normal curve exactly in half, leaving 0.5 of the area to the right.
15. A good player is not selected in the team, is an example of:
(A) Type I-error (B) Type II-error (C) Sampling error (D) Bias
Correct Answer: (B) Type II-error — Failing to select a genuinely deserving candidate means failing to reject a false null hypothesis, which is a Type II error.
16. For (r × c) contingency table the degree of freedom should be:
(A) "rc" (B) (r − 1)c (C) (c − 1)r (D) (r − 1)(c − 1)
Correct Answer: (D) (r − 1)(c − 1) — Degrees of freedom for a contingency table = (rows − 1)(columns − 1).
17. Finite population correction factor is:
(A) n/N (B) N/n (C) (N − n)/(N − 1) (D) (n − N)/(N − 1)
Correct Answer: (C) (N − n)/(N − 1) — The finite population correction factor, used to adjust the standard error for sampling without replacement, is (N − n)/(N − 1).
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