Post RN BSN Biostatistics – Unit III Presenting Data Solved Answers

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Posted by POST RN BSN Resources · Original syllabus post: May 4, 2017 · Category: Post RN BSN Nursing Course Syllabus

Post RN BSN Nursing – Biostatistics, Course No. 717 – Part 3 of 6. Expanded exam-style model answers for Unit III of the LUMHS Post RN BSN biostatistics syllabus: frequency and contingency tables, bar charts, frequency distributions, histograms, frequency polygons, stem-and-leaf plots and box-and-whisker plots, with charts drawn from worked examples. Use them as a study guide and write in your own words in the exam hall.

Please note: The syllabus lists topics only. These are exam-style questions and model answers prepared from those topics; they are not an official LUMHS paper or answer key. Worked examples use made-up numbers for practice.

📚 Course syllabus: Biostatistics (Course No. 717), LUMHS Post RN BSN – read the full course syllabus here.

Biostatistics Unit III Presenting Data Solved | Post RN BSN Use as a revision guide and verify with your course notes.

Unit III: Presenting Data

Course syllabus · Model exam answers

B.Sc NURSING (POST-RN), SECOND YEAR, SEMESTER-III

BIOSTATISTICS – COURSE NO. 717

UNIT III: PRESENTING DATA

Credit hours: 3

Evaluation: Assignment 10%, Internal 10%, Final 80%

Source: course syllabus

Syllabus topics: Tables and graphs for nominal and ordinal data (frequency and contingency tables, bar chart); tables and graphs for numerical data; stem-and-leaf plot; frequency tables; histograms, box-and-whisker plots and frequency polygons.

Note: all data in the examples are made up for practice (haemoglobin of 30 women, admissions of one ward). The charts in this article were drawn from those numbers.

Q-1. Why is data presented in tables and graphs? State the principles of good data presentation.

Raw data are difficult to read. Presentation arranges data in tables, charts and graphs so that patterns, comparisons and trends can be seen quickly and communicated clearly.

Principles

Choose the display that matches the type (scale) of data.
Give every table or graph a clear, self-explanatory title (what, where, when).
Label rows, columns, axes and units.
Keep it simple: one main message per display.
Use a proper scale; the vertical axis of a bar chart should start at zero.
Show totals and percentages where useful.
Give the source of the data.
Avoid decoration or 3-D effects that distort the picture.

Type of data	Table	Graph
Nominal and ordinal (categories)	Frequency table, contingency (cross-tabulation) table	Bar chart (simple, multiple, component), pie chart
Numerical (discrete or continuous)	Frequency distribution with class intervals	Histogram, frequency polygon, box-and-whisker plot, stem-and-leaf plot, line graph, scatter diagram

Q-2. Construct a frequency table for nominal data. Explain relative and cumulative frequency.

A frequency table lists each category and the number of observations in it. Example: diagnoses of 160 patients admitted to a medical ward in a month (made-up data).

Diagnosis	Frequency (f)	Relative frequency	Percentage
Respiratory infection	48	0.300	30.0%
Gastroenteritis	36	0.225	22.5%
Hypertension	30	0.1875	18.8%
Diabetes	24	0.150	15.0%
Injuries	22	0.1375	13.8%
Total	160	1.000	100%

Frequency: the count in a category.
Relative frequency: frequency ÷ total (f ÷ n); the percentage is relative frequency × 100.
Cumulative frequency: running total of frequencies; meaningful only when categories have a natural order (ordinal data or numerical classes).

Percentages should add up to about 100% (rounding may cause small differences).

Q-3. Describe the bar chart. State its types and rules of construction.

A bar chart displays the frequency (or percentage) of each category of nominal or ordinal data by bars of equal width separated by gaps. The length of each bar is proportional to the frequency.

Bar chart of admissions by diagnosis (made-up data from the frequency table above).

Type	Use
Simple bar chart	One variable (diagnosis)
Multiple (clustered) bar chart	Compare groups side by side (diagnosis by sex)
Component (stacked) bar chart	Each bar divided into parts (e.g. proportion of outcomes within each diagnosis)
Percentage bar chart	Compare relative composition of groups of different size

Rules

Equal width bars with equal gaps.
Start the scale at zero.
Arrange categories logically (e.g. by size or natural order).
Label both axes and give a title.
Use the same scale for charts that will be compared.

Q-4. Write short notes on the pie chart and the pictogram.

Pie chart: a circle divided into sectors whose angles are proportional to the share of each category. Angle = (category frequency ÷ total) × 360°. Example: respiratory infection = (48 ÷ 160) × 360° = 108°. Best for a few categories that make up a whole; unsuitable when there are many categories or when differences are small.

Pictogram: uses small pictures, each representing a fixed number of cases (e.g. one bed symbol = 10 patients). Attractive for community health education but less exact.

Q-5. What is a contingency (cross-tabulation) table? Construct and interpret one.

A contingency table shows the frequencies of two categorical variables together: one defines the rows and the other the columns. It is used to study the relationship between them (analysed with the chi-square test in Unit V).

Example (made-up): 100 patients with surgical wounds were dressed with dressing A or dressing B, and wound infection was recorded.

Dressing	Infection	No infection	Total	Infection rate (row %)
A	8	42	50	16%
B	18	32	50	36%
Total	26	74	100	26%

Interpretation: infection occurred in 16% of wounds with dressing A and 36% with dressing B. This is an association; whether the difference is real (not due to chance) must be tested statistically.

Tips

Give row or column percentages so that groups of different size can be compared.
Show marginal totals.
A 2 × 2 table has two rows and two columns.

Q-6. How are ordinal data presented?

Ordinal data (e.g. pain: none, mild, moderate, severe) are presented with a frequency table in the natural order of the categories, with cumulative percentages, and a bar chart with bars arranged in that order (not a pie chart sorted by size).

Pain grade	Patients	%	Cumulative %
None	10	10%	10%
Mild	30	30%	40%
Moderate	40	40%	80%
Severe	20	20%	100%
Total	100	100%

The cumulative column shows, for example, that 80% of patients had moderate pain or less. The median category can be read from it (the 50th percentile falls in “moderate”). Data are made up.

Q-7. Explain how to construct a frequency distribution (frequency table) for numerical data.

When numerical data have many different values they are grouped into class intervals. Example: haemoglobin (g/dL) of 30 pregnant women (made-up): 8.2, 8.9, 9.1, 9.4, 9.6, 9.8, 10.0, 10.1, 10.3, 10.4, 10.5, 10.6, 10.8, 10.9, 11.0, 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.8, 11.9, 12.0, 12.1, 12.3, 12.5, 12.8, 13.2, 13.6.

Steps

Find the range = largest − smallest = 13.6 − 8.2 = 5.4.
Decide the number of classes, usually 5–15. Sturges’ rule: k = 1 + 3.322 log₁₀n = 1 + 3.322 × log₁₀30 ≈ 5.9, so use 6 classes.
Class width ≈ range ÷ k = 5.4 ÷ 6 = 0.9, rounded to a convenient 1.0 g/dL.
Write non-overlapping classes covering all values (8.0–8.9, 9.0–9.9 …).
Tally the values and count the frequency of each class.
Add relative and cumulative frequency; check that the total is 30.

Class (g/dL)	Midpoint	Frequency	Relative %	Cumulative frequency
8.0–8.9	8.45	2	6.7%	2
9.0–9.9	9.45	4	13.3%	6
10.0–10.9	10.45	8	26.7%	14
11.0–11.9	11.45	9	30.0%	23
12.0–12.9	12.45	5	16.7%	28
13.0–13.9	13.45	2	6.7%	30
Total		30	100%

Terms: class limits are the stated lowest and highest values of a class (8.0 and 8.9); class boundaries are the true limits that remove the gap between classes (7.95 and 8.95); midpoint = (lower + upper limit) ÷ 2; class width = difference between successive lower limits.

Rules: classes must be mutually exclusive and exhaustive, preferably of equal width, with no open-ended classes where possible.

Q-8. Describe the histogram. How is it constructed and what are its uses?

A histogram is a graph of a frequency distribution of continuous numerical data. Each class is a rectangle; the bars touch each other because the scale is continuous, and the area of each bar is proportional to the frequency (with equal class widths, the height is proportional too).

Histogram of haemoglobin of 30 women (made-up data).

Construction

Draw the horizontal axis (class boundaries) and the vertical axis (frequency).
Draw a bar for each class with no gaps.
Label axes and give a title.

Uses

Shows the shape of the distribution: symmetrical, skewed, one or two peaks.
Shows the centre and spread.
Identifies gaps and unusual values.
Gives a quick check of whether the data look approximately normal.

Interpretation of this histogram: most women have haemoglobin of 10–11.9 g/dL; the distribution is roughly symmetrical with a slight tail to higher values.

Q-9. Describe the frequency polygon. How is it drawn?

A frequency polygon is a line graph formed by joining the midpoints of the tops of histogram bars; it is closed at both ends by adding an empty class (frequency 0) before the first and after the last class.

Frequency polygon (red line) drawn over the histogram of the same data.

Steps

Calculate the midpoint of every class.
Plot (midpoint, frequency) points.
Add one extra class at each end with frequency 0 and plot those points on the axis.
Join the points with straight lines.

Advantages: several distributions can be drawn on the same graph for comparison (e.g. haemoglobin before and after iron treatment); suitable for large data; shows the shape clearly. Note: a cumulative frequency polygon (ogive) uses cumulative frequencies and is used to find the median and percentiles.

Q-10. Describe the stem-and-leaf plot. Construct one.

A stem-and-leaf plot shows the actual data values arranged in order, like a histogram turned sideways. Each value is split into a stem (leading digits) and a leaf (last digit).

Stem | Leaf 8 | 2 9 9 | 1 4 6 8 10 | 0 1 3 4 5 6 8 9 11 | 0 1 2 3 4 5 6 8 9 12 | 0 1 3 5 8 13 | 2 6 Key: 10 | 2 means 10.2 g/dL

Steps

Sort the data.
Choose the stems (here the whole number part).
Write the leaf (decimal digit) of each value beside its stem, in increasing order.
Add a key.

Advantages: keeps the original values; easy for small and medium data sets (up to about 50 values); shows the shape, median and outliers at a glance. Limitation: unsuitable for very large data.

Reading the plot: the longest rows are stems 10 and 11, showing where most values lie; the median lies between the 15th and 16th values (11.0 and 11.1), so the median = 11.05 g/dL.

Q-11. Describe the box-and-whisker plot. Explain the five-number summary.

A box-and-whisker plot (box plot) summarizes a numerical distribution using five numbers: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum.

Box-and-whisker plot of haemoglobin of 30 women (made-up data).

Statistic	Value (g/dL)	Meaning
Minimum	8.2	Smallest value
Q1 (25th percentile)	10.1	25% of values are below this
Median (Q2)	11.05	Middle value; 50% below
Q3 (75th percentile)	11.9	75% of values are below this
Maximum	13.6	Largest value
Interquartile range (IQR)	1.8	Q3 − Q1: spread of the middle 50%

Method used: Q1 and Q3 are the medians of the lower and upper 15 values (other software may give slightly different quartiles).

Construction and reading

Draw a box from Q1 to Q3 and a line at the median.
Whiskers extend to the smallest and largest values that are not outliers.
Outliers lie below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR (here the fences are 7.40 and 14.60, so there are no outliers).
If the median is near the centre of the box and the whiskers are similar in length, the distribution is roughly symmetrical; if the median is closer to one end, the data are skewed.

Advantages: compact, good for comparing several groups side by side (for example haemoglobin in three wards), and does not depend on the mean.

Q-12. Differentiate between a bar chart and a histogram.

Point	Bar chart	Histogram
Data	Nominal or ordinal (categories); also discrete	Continuous numerical, grouped in classes
Bars	Separated by gaps	Touching; no gaps
Order of bars	Can be rearranged (for nominal)	Fixed by the numerical scale
Width of bar	No numerical meaning	Represents the class width
What is proportional	Length of bar	Area of bar
Example	Admissions by diagnosis	Haemoglobin levels

Q-13. Compare histogram, frequency polygon, stem-and-leaf plot and box plot. Which would you choose?

Display	Best for	Shows actual values?	Compares groups?
Histogram	Shape of one large distribution	No	Hard
Frequency polygon	Comparing two or more distributions on one graph	No	Yes
Stem-and-leaf plot	Small data sets; shape plus actual values	Yes	Hard
Box-and-whisker plot	Median, spread and outliers; comparing many groups	No	Yes (best)

Rule of thumb: small data → stem-and-leaf; one large data set → histogram; comparing groups → box plots or polygons.

Q-14. Write short notes on the line graph and the scatter diagram.

Line graph: shows change over time (a time series) by joining points. Example: the patient’s temperature chart, monthly admissions, or yearly infant mortality rate. Time is on the horizontal axis.

Scatter diagram: plots pairs of numerical values (e.g. weight and blood pressure) to see if two variables are related; the pattern may be rising (positive), falling (negative) or none. It does not prove cause and effect.

Q-15. Write the rules for constructing good tables. How are graphs made misleading?

Rules for a table

A clear number and title.
Headings for rows and columns with units.
Data arranged logically (size, time, or natural order).
Totals and percentages.
Footnotes and source.
Not overcrowded.

How graphs mislead

Cutting the vertical axis so small differences look large.
Unequal scales or class widths in a histogram.
3-D effects and pictures that distort areas.
Missing labels or titles.
Choosing the time period to show only a favourable trend.

Q-16. Practice exercise: pulse rates of 10 patients are 72, 68, 80, 76, 74, 88, 92, 70, 76, 82. Draw a stem-and-leaf plot and find the median and range.

Sorted: 68, 70, 72, 74, 76, 76, 80, 82, 88, 92.

Stem | Leaf 6 | 8 7 | 0 2 4 6 6 8 | 0 2 8 9 | 2 Key: 7 | 2 means 72 beats/min

Median: n = 10, so the median is the average of the 5th and 6th values = (76 + 76) ÷ 2 = 76 beats per minute.

Range: 92 − 68 = 24 beats per minute.

Q-17. How does a nurse use data presentation in practice?

Charting vital signs (line graphs) and fluid balance.
Presenting ward statistics in meetings (bar charts, tables): infections, falls, pressure injuries, bed occupancy.
Community health surveys and immunization coverage charts.
Reporting nursing research results.
Health education posters with simple charts and pictograms.
Audit and quality-improvement reports.

Conclusion: Choosing the right table or graph makes data clear, honest and useful for decisions.

Course references (as listed in the syllabus): Saunders, B. D., & Trapp, R. C. (1994). Basic and Clinical Biostatistics (2nd ed.). New Delhi: Prentice-Hall.

Source syllabus: Course Syllabus – LUMHS Post RN BSN Bio-Statistic (original post dated May 4, 2017).

Series (Biostatistics, Course No. 717): Part 1: Unit I – Introduction to Biostatistics. Part 2: Unit II – Scales of Measurement. Part 3: Unit III – Presenting Data. Part 4: Unit IV – Summarizing Data. Part 5: Unit V – Making Inference from Data. Part 6: Biostatistics for Nurses – facts, skills, uses, benefits and hurdles.

Independent educational resource: POST RN BSN Nursing Resources is not affiliated with, endorsed by or an official publication of LUMHS or PNMC. Model answers are study aids; verify against your course notes and textbooks.

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