Frequency distribution and graphical representation of data are essential topics for B.Pharm students learning to summarize and interpret experimental, clinical, and quality-control datasets. This introduction covers core concepts such as grouped and ungrouped frequency tables, class intervals, class width, midpoints, cumulative and relative frequency, and common plots—histogram, frequency polygon, ogive, bar chart, and pie chart. Emphasis is placed on choosing appropriate graphical tools for continuous versus categorical data, calculating measures (mean, median, mode) from grouped data, and understanding how visual representation reveals skewness, dispersion, and outliers in pharmaceutical data. Now let’s test your knowledge with 30 MCQs on this topic.
Q1. What is a frequency distribution?
- A table that shows how often each value or class occurs in a dataset
- A method to calculate the mean and standard deviation
- A graphical plot only used for continuous variables
- A list of every individual observation without summarizing
Correct Answer: A table that shows how often each value or class occurs in a dataset
Q2. Which term describes the midpoint of a class interval?
- Class boundary
- Class width
- Class mark
- Class limit
Correct Answer: Class mark
Q3. What is the class width (class size)?
- The difference between the upper and lower class boundaries
- The number of classes in a frequency table
- The cumulative frequency of a class
- The midpoint of a class interval
Correct Answer: The difference between the upper and lower class boundaries
Q4. Which plot is most appropriate for showing distribution of continuous data with class intervals?
- Bar chart with gaps between bars
- Histogram with contiguous bars
- Pie chart
- Scatter plot
Correct Answer: Histogram with contiguous bars
Q5. What does a frequency polygon display?
- Individual raw data points connected by lines
- Class midpoints connected by straight lines using class frequencies
- A circular representation of proportions
- The same as a pie chart for categorical data
Correct Answer: Class midpoints connected by straight lines using class frequencies
Q6. In an ogive, the plotted values represent:
- Relative frequencies for each class
- Cumulative frequencies up to each upper class boundary
- Class midpoints versus frequency density
- The mode for each class interval
Correct Answer: Cumulative frequencies up to each upper class boundary
Q7. Which is a key difference between grouped and ungrouped frequency distributions?
- Grouped data lists every observation; ungrouped groups observations
- Grouped data summarizes values into class intervals; ungrouped lists raw values
- Ungrouped data cannot be used to compute central tendency
- Grouped distribution is only for categorical variables
Correct Answer: Grouped data summarizes values into class intervals; ungrouped lists raw values
Q8. Relative frequency is defined as:
- The proportion of observations in a class divided by the total number of observations
- The cumulative total of frequencies across all classes
- The absolute difference between class limits
- The width of each class interval
Correct Answer: The proportion of observations in a class divided by the total number of observations
Q9. Frequency density is used when class widths are unequal; it equals:
- Frequency × class width
- Frequency ÷ class width
- Cumulative frequency ÷ class midpoint
- Relative frequency × 100
Correct Answer: Frequency ÷ class width
Q10. Which rule is commonly used to estimate the number of class intervals?
- Chebyshev’s rule
- Sturges’ rule
- Empirical rule (68-95-99.7)
- Central limit theorem
Correct Answer: Sturges’ rule
Q11. When constructing a grouped frequency table for continuous data, you should:
- Choose overlapping class intervals for clarity
- Ensure class boundaries are mutually exclusive and exhaustive
- Use arbitrarily large class widths to reduce classes
- Always use ten classes regardless of sample size
Correct Answer: Ensure class boundaries are mutually exclusive and exhaustive
Q12. Which graphical method is best for comparing frequencies of categories (nominal data)?
- Histogram
- Pie chart or bar chart
- Ogive
- Frequency polygon
Correct Answer: Pie chart or bar chart
Q13. How is the median estimated from grouped data?
- Using raw sorted data only
- By linear interpolation within the median class using cumulative frequency
- By finding the highest frequency class
- By averaging all class midpoints
Correct Answer: By linear interpolation within the median class using cumulative frequency
Q14. The mode for grouped frequency data is estimated using:
- Arithmetic mean of class midpoints
- The midpoint of the median class
- The formula involving the modal class and frequencies of adjacent classes
- Cumulative frequency divided by total frequency
Correct Answer: The formula involving the modal class and frequencies of adjacent classes
Q15. What does a right-skewed (positively skewed) histogram indicate?
- Tail extends to the left, with majority of values high
- Tail extends to the right, with majority of values low
- Perfectly symmetric distribution
- Data are uniformly distributed
Correct Answer: Tail extends to the right, with majority of values low
Q16. Which of the following is TRUE about cumulative relative frequency?
- It decreases as class intervals increase
- It shows the running total of relative frequencies up to a class
- It equals the frequency density multiplied by class width
- It is used only for categorical variables
Correct Answer: It shows the running total of relative frequencies up to a class
Q17. Which error affects the visual interpretation of a histogram?
- Using frequency polygon instead of histogram
- Choosing unequal class widths without adjusting frequency density
- Labeling axes with units
- Plotting cumulative frequency as ogive
Correct Answer: Choosing unequal class widths without adjusting frequency density
Q18. For discrete count data (e.g., number of tablets), the preferred chart is:
- Histogram with class intervals of 0.5 units
- Bar chart with gaps between bars
- Ogive
- Frequency polygon with smooth curve
Correct Answer: Bar chart with gaps between bars
Q19. In pharmacology lab data, why use grouped frequency distribution?
- To hide variability in data
- To simplify and summarize large continuous datasets for analysis and visualization
- Because raw data cannot be used for statistics
- To eliminate outliers automatically
Correct Answer: To simplify and summarize large continuous datasets for analysis and visualization
Q20. Which statistic can be estimated directly from a frequency distribution table?
- Exact individual measurement values
- Sample mean using class midpoints and frequencies
- Population variance without frequencies
- Exact median without interpolation
Correct Answer: Sample mean using class midpoints and frequencies
Q21. What is an open-ended class in grouped data?
- A class with both upper and lower limits specified
- A class with no specified lower or upper boundary (e.g., “≥ 100”)
- A class that contains only one observation
- A class used only for nominal variables
Correct Answer: A class with no specified lower or upper boundary (e.g., “≥ 100”)
Q22. When converting a frequency table into a relative frequency table, sum of relative frequencies equals:
- Total number of classes
- Zero
- One (or 100% if expressed as percentage)
- Mean frequency
Correct Answer: One (or 100% if expressed as percentage)
Q23. The cumulative frequency curve used to estimate percentiles is called:
- Histogram
- Ogive
- Scatter plot
- Bar chart
Correct Answer: Ogive
Q24. Which choice correctly describes class boundaries?
- They are the rounded class midpoints
- They remove gaps between consecutive classes by adjusting limits by 0.5 of unit scale
- They are only used for categorical data
- They are identical to class labels
Correct Answer: They remove gaps between consecutive classes by adjusting limits by 0.5 of unit scale
Q25. Which graphical representation is least useful for showing distribution shape?
- Histogram
- Pie chart
- Frequency polygon
- Ogive
Correct Answer: Pie chart
Q26. In a grouped frequency table, total frequency equals:
- Sum of class midpoints
- Sum of all class frequencies
- Difference between highest and lowest class limits
- Number of class intervals
Correct Answer: Sum of all class frequencies
Q27. Which is an advantage of graphical representation of pharmaceutical data?
- It replaces the need for statistical tests
- It helps detect patterns, skewness, and outliers visually
- It guarantees accurate conclusions without calculations
- It always eliminates measurement error
Correct Answer: It helps detect patterns, skewness, and outliers visually
Q28. What does frequency table grouping affect most directly?
- The chemical composition of samples
- The apparent shape and summary measures of the distribution
- The physical units of measurement
- The pharmacological potency of a drug
Correct Answer: The apparent shape and summary measures of the distribution
Q29. Which measure can be read from a histogram but not directly from a frequency table without calculation?
- Exact cumulative frequency values
- Visual impression of modality (uni-, bi-, multimodal)
- Class frequencies
- Total sample size
Correct Answer: Visual impression of modality (uni-, bi-, multimodal)
Q30. When presenting adverse event categories in a clinical trial, the best initial summary is:
- Ungrouped frequency distribution of each patient’s full laboratory data
- Categorical frequency table with counts and percentages, then bar chart
- Ogive of laboratory values
- Frequency polygon of continuous pharmacokinetic parameters
Correct Answer: Categorical frequency table with counts and percentages, then bar chart
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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