Introduction: Measures of central tendency — mean, median, and mode — are essential statistical tools in pharmaceutical research and quality control. For B. Pharm students, understanding how these measures summarize data from assays, dissolution tests, bioavailability studies, particle size analysis, and stability studies is crucial. Accurate use of mean, median, mode, geometric mean, and harmonic mean helps interpret skewed concentrations, MIC distributions, batch uniformity, and rate-based parameters like clearance. This topic links statistical analysis to drug formulation, quality control, and regulatory reporting. Practicing targeted MCQs strengthens decision-making when data are skewed, multimodal, or weighted. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. Which measure of central tendency is most appropriate for skewed drug concentration data with outliers?
- Arithmetic mean
- Mode
- Median
- Geometric mean
Correct Answer: Median
Q2. For minimum inhibitory concentration (MIC) values that are multiplicative and span several orders of magnitude, which measure is preferred?
- Arithmetic mean
- Median
- Geometric mean
- Mode
Correct Answer: Geometric mean
Q3. In content uniformity testing of tablets where a few capsules show extreme potency, which robust statistic gives a better central estimate?
- Arithmetic mean of all units
- Trimmed mean (e.g., 10% trimmed)
- Mode of potency values
- Median absolute deviation
Correct Answer: Trimmed mean (e.g., 10% trimmed)
Q4. When reporting average particle size from a log-normal distribution, which central measure often better represents central tendency?
- Arithmetic mean
- Median
- Geometric mean
- Mode
Correct Answer: Geometric mean
Q5. Which measure of central tendency is most appropriate for categorical pharmaceutical data such as dosage form preference?
- Median
- Mode
- Arithmetic mean
- Geometric mean
Correct Answer: Mode
Q6. In a dissolution profile with two prominent peaks in percent dissolved at different time points, which concept explains the presence of two common values?
- Skewness
- Multimodality
- High variance
- Homoscedasticity
Correct Answer: Multimodality
Q7. Which central tendency measure minimizes the sum of squared deviations from data points and is the basis for many parametric tests?
- Median
- Mode
- Arithmetic mean
- Geometric mean
Correct Answer: Arithmetic mean
Q8. For pooled bioavailability studies with known sample sizes per study, which mean accounts for differing sample sizes?
- Geometric mean
- Simple arithmetic mean
- Weighted mean
- Median
Correct Answer: Weighted mean
Q9. Which measure remains unchanged by any monotonic increasing transformation of the data (e.g., log transform) when comparing relative changes?
- Arithmetic mean
- Median
- Mode
- Geometric mean
Correct Answer: Median
Q10. In pharmacokinetics, which average is commonly used for reporting half-life when half-lives are calculated multiplicatively across subjects?
- Arithmetic mean half-life
- Geometric mean half-life
- Mode of half-lives
- Median absolute deviation
Correct Answer: Geometric mean half-life
Q11. When a dataset has a highest frequency at a particular assay value, which central measure identifies that value?
- Mean
- Median
- Mode
- Geometric mean
Correct Answer: Mode
Q12. If a batch weight distribution is symmetric and unimodal, which measure will equal the other two (mean, median, mode)?
- Only mean equals median
- Only mode equals median
- Mean, median, and mode are all equal
- None of them are equal
Correct Answer: Mean, median, and mode are all equal
Q13. For rates such as clearance (volume per time) averaged across study periods, which mean can be more appropriate than arithmetic mean?
- Geometric mean
- Harmonic mean
- Mode
- Median
Correct Answer: Harmonic mean
Q14. Which measure is least affected by extreme high values when summarizing potency assay results?
- Arithmetic mean
- Median
- Standard deviation
- Variance
Correct Answer: Median
Q15. When combining log-transformed pharmacokinetic parameters and exponentiating the mean of logs, which central tendency is obtained?
- Arithmetic mean
- Median
- Geometric mean
- Mode
Correct Answer: Geometric mean
Q16. In a stability study showing a long right tail due to degradants, which summary statistic guides a regulator about the central trend without influence from tail?
- Arithmetic mean
- Median
- Mode
- Range
Correct Answer: Median
Q17. Which measure is most useful when reporting the most common adverse event category in a clinical trial?
- Mean severity score
- Median time to event
- Mode of categories
- Geometric mean of rates
Correct Answer: Mode of categories
Q18. For grouped frequency data from tablet weights, which method estimates the median within a class interval?
- Interpolated median formula for grouped data
- Arithmetic mean of class midpoints
- Mode of class midpoints
- Sum of cumulative frequencies
Correct Answer: Interpolated median formula for grouped data
Q19. When comparing two formulations with skewed dissolution times, which test uses medians rather than means?
- Independent t-test
- Mann–Whitney U test (Wilcoxon rank-sum)
- Paired t-test
- ANOVA
Correct Answer: Mann–Whitney U test (Wilcoxon rank-sum)
Q20. For concentration-time data with frequent zeros (below detection), which central tendency might mislead if zeros are omitted?
- Median
- Mode
- Arithmetic mean
- Geometric mean
Correct Answer: Arithmetic mean
Q21. Which mean is appropriate for averaging speeds or rates, such as dosing rates, where reciprocal averaging is required?
- Arithmetic mean
- Geometric mean
- Harmonic mean
- Mode
Correct Answer: Harmonic mean
Q22. In a dataset of potency values showing two peaks, which summary statistic would hide the dual peaks?
- Mode
- Median
- Histogram inspection
- Arithmetic mean
Correct Answer: Arithmetic mean
Q23. When data are weighted by subject reliability (e.g., assay precision), which central measure properly incorporates weights?
- Simple arithmetic mean
- Weighted mean
- Median
- Mode
Correct Answer: Weighted mean
Q24. For log-normally distributed pharmacokinetic AUC values, which measure yields a central value closer to typical patient exposure?
- Arithmetic mean AUC
- Geometric mean AUC
- Mode of AUC
- Median absolute deviation
Correct Answer: Geometric mean AUC
Q25. Which central tendency is most sensitive to every data value and thus most affected by a single extreme measurement?
- Median
- Mode
- Arithmetic mean
- Geometric mean
Correct Answer: Arithmetic mean
Q26. For multiple assay runs with varying precision, which approach ensures runs with higher precision influence the central estimate more?
- Compute unweighted mean across runs
- Use median of run means
- Use inverse-variance weighted mean
- Pick the mode of run means
Correct Answer: Use inverse-variance weighted mean
Q27. In reporting a central value for fold-changes in enzyme activity across subjects, which mean is conceptually appropriate?
- Arithmetic mean of fold-changes
- Median of fold-changes
- Geometric mean of fold-changes
- Mode of fold-changes
Correct Answer: Geometric mean of fold-changes
Q28. Which central tendency is best when the goal is to report the most representative single value for symmetric continuous assay results?
- Mode
- Median
- Arithmetic mean
- Geometric mean
Correct Answer: Arithmetic mean
Q29. If assay data are heavily left-skewed due to lower-limit censoring, which summary is often misleading if censoring is ignored?
- Median
- Arithmetic mean
- Mode
- Trimmed mean
Correct Answer: Arithmetic mean
Q30. For reporting central tendency of multiplicative bioassay titers where values are log-transformed for analysis, which back-transformed estimate should be presented?
- Arithmetic mean of original titers
- Median of original titers
- Exponentiated mean of log titers (geometric mean)
- Mode of original titers
Correct Answer: Exponentiated mean of log titers (geometric mean)
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.
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