Measures of dispersion – range, standard deviation and variance MCQs With Answer

Measures of dispersion—range, standard deviation and variance—are essential components of descriptive statistics in pharmaceutical studies. B.Pharm students must understand how data variability affects drug quality, assay reproducibility, formulation uniformity and stability testing. The range provides a quick spread indicator, variance quantifies average squared deviation, and standard deviation gives dispersion in original units, aiding interpretation of batch consistency and analytical precision. Mastering these concepts helps in quality control, bioequivalence studies, and interpreting experimental errors. This set of focused MCQs emphasises calculation, interpretation, sensitivity to outliers, and real-world pharmaceutical applications to strengthen your statistical reasoning. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. Which measure of dispersion gives the simplest indication of spread by subtracting the smallest value from the largest?

• Variance
• Standard deviation
• Range
• Coefficient of variation

Correct Answer: Range

Q2. Which statement about variance is true in the context of pharmaceutical assay results?

• Variance is expressed in the same units as the original data
• Variance equals the square root of the standard deviation
• Variance quantifies average squared deviations from the mean
• Variance is unaffected by outliers

Correct Answer: Variance quantifies average squared deviations from the mean

Q3. Why is standard deviation often preferred over variance for reporting dispersion?

• Standard deviation is always smaller than variance
• Standard deviation is in the same units as the data, making interpretation easier
• Standard deviation ignores the mean
• Standard deviation is unaffected by sample size

Correct Answer: Standard deviation is in the same units as the data, making interpretation easier

Q4. In a batch weight study you find SD = 2 mg and mean = 50 mg. What is the coefficient of variation (CV)?

• 0.04%
• 4%
• 2%
• 25%

Correct Answer: 4%

Q5. Which formula represents the sample variance (unbiased estimator) for a dataset of n observations?

• σ² = Σ(x – μ)² / n
• s² = Σ(x – x̄)² / (n – 1)
• s = √(Σ(x – x̄) / n)
• σ = Σ|x – x̄| / n

Correct Answer: s² = Σ(x – x̄)² / (n – 1)

Q6. If every dissolution time in a dataset is multiplied by 10, how does the variance change?

• Variance remains the same
• Variance is multiplied by 10
• Variance is multiplied by 100
• Variance becomes the square root of original variance

Correct Answer: Variance is multiplied by 100

Q7. Which measure is most sensitive to a single extreme outlier in tablet assay values?

• Median absolute deviation
• Interquartile range
• Range
• Mode

Correct Answer: Range

Q8. What is the relationship between variance (σ²) and standard deviation (σ)?

• σ² = σ + mean
• σ² = σ² / n
• σ = √(σ²)
• σ = (σ²)²

Correct Answer: σ = √(σ²)

Q9. For normally distributed assay results, approximately what percentage falls within ±1 standard deviation of the mean?

• 50%
• 68%
• 95%
• 99.7%

Correct Answer: 68%

Q10. Which dispersion measure is dimensionless and useful for comparing variability across different units (e.g., mg vs mL)?

• Variance
• Standard deviation
• Range
• Coefficient of variation

Correct Answer: Coefficient of variation

Q11. When calculating sample variance, why divide by (n−1) rather than n?

• To make the estimator biased
• To correct for using the sample mean instead of the true mean (unbiased estimation)
• Because population variance is unknown
• To reduce the numerical value

Correct Answer: To correct for using the sample mean instead of the true mean (unbiased estimation)

Q12. If the standard deviation of potency measurements is 0, what does that indicate?

• All measurements are identical
• Half of measurements are outliers
• Data is highly variable
• Mean is zero

Correct Answer: All measurements are identical

Q13. Which concept describes the average distance of observations from the mean in original units?

• Variance
• Standard deviation
• Range squared
• Pooled variance

Correct Answer: Standard deviation

Q14. In inter-laboratory precision studies, which dispersion measure helps compare relative variability between labs?

• Interquartile range
• Coefficient of variation
• Absolute deviation
• Range

Correct Answer: Coefficient of variation

Q15. A dataset: 98, 100, 102. What is the range?

• 2
• 4
• 100
• 6

Correct Answer: 4

Q16. Which rule gives bounds for any distribution, stating at least 75% of values lie within 2 SD of the mean?

• Empirical rule
• Chebyshev’s theorem
• Central limit theorem
• Law of large numbers

Correct Answer: Chebyshev’s theorem

Q17. How does adding a constant to every observation affect the standard deviation?

• Increases SD by the constant
• Multiplies SD by the constant
• Leaves SD unchanged
• Square roots the SD

Correct Answer: Leaves SD unchanged

Q18. Which is true about units of variance compared to original measurements?

• Variance has the same units as original data
• Variance has squared units of the original data
• Variance is unitless
• Variance units are the square root of original units

Correct Answer: Variance has squared units of the original data

Q19. In comparing two formulations, formulation A has SD = 1 mg, formulation B has SD = 3 mg. Which is more precise?

• Formulation A
• Formulation B
• Both are equally precise
• Cannot determine without mean

Correct Answer: Formulation A

Q20. Which dispersion measure is robust to extreme values and often used with medians?

• Range
• Standard deviation
• Interquartile range
• Variance

Correct Answer: Interquartile range

Q21. What happens to the standard deviation when sample size increases but variability pattern stays the same?

• SD necessarily increases
• SD necessarily decreases
• SD tends to stabilize around the population SD
• SD becomes zero

Correct Answer: SD tends to stabilize around the population SD

Q22. Which formula gives pooled variance for two independent samples with variances s1², s2² and sizes n1, n2?

• (s1² + s2²)/2
• [(n1−1)s1² + (n2−1)s2²] / (n1 + n2 − 2)
• s1²/n1 + s2²/n2
• √(s1² + s2²)

Correct Answer: [(n1−1)s1² + (n2−1)s2²] / (n1 + n2 − 2)

Q23. Which is a correct interpretation: “SD = 5 mg” for tablet weights?

• Typical deviation from the mean weight is about 5 mg
• All tablets differ from mean by exactly 5 mg
• Mean weight is 5 mg
• Variance is 5 mg

Correct Answer: Typical deviation from the mean weight is about 5 mg

Q24. Which dispersion measure would you check first when evaluating batch uniformity from a quick glance?

• Standard deviation
• Range
• Variance
• Skewness

Correct Answer: Range

Q25. If two processes have equal means but different variances, what does that imply?

• They have different average values
• One process shows greater variability around the same average
• The process with higher variance has a higher median
• They must have different sample sizes

Correct Answer: One process shows greater variability around the same average

Q26. Which of the following is NOT a property of standard deviation?

• Always non-negative
• Measures dispersion around the mean
• Additive when summing independent variables
• Increases when spread increases

Correct Answer: Additive when summing independent variables

Q27. When replacing outliers by a robust central value, which dispersion measure will typically change the least?

• Range
• Standard deviation
• Interquartile range
• Variance

Correct Answer: Interquartile range

Q28. Which statistic describes variability of the sample mean across repeated samples?

• Sample variance
• Standard deviation of individual observations
• Standard error of the mean
• Range of observations

Correct Answer: Standard error of the mean

Q29. Two labs report SDs for an assay: Lab A SD = 0.5% of mean, Lab B SD = 1.0% of mean. Which lab shows better precision?

• Lab A
• Lab B
• Both equal
• Precision cannot be compared using SD

Correct Answer: Lab A

Q30. Which statement is true about variance when combining two independent random variables X and Y?

• Var(X+Y) = Var(X) + Var(Y) if X and Y are independent
• Var(X+Y) = Var(X) − Var(Y) always
• Var(X+Y) = [Var(X) + Var(Y)] / 2
• Var(X+Y) equals the covariance only

Correct Answer: Var(X+Y) = Var(X) + Var(Y) if X and Y are independent

G S Sachin

I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.

Mail- Sachin@pharmacyfreak.com