Chapter 12 · Collecting and showing data

How do you show data in a picture?

Tables, diagrams and graphs, and which one fits which data.

8 TNMGRMU questions answered hereset 10 times, 2002–2023

The problem first

You are a second-year MD Community Medicine resident presenting your anaemia survey at the department meeting. Your slides show a 3-D pie chart of anaemia grades, a histogram of the same four grades, and a bar chart of mean haemoglobin in rural and urban girls with the axis starting at 10.8 g/dL.

The professor looks at the slides for a few seconds and asks one question.

“Why did you choose these charts for these data?”

Start here

Should the numbers go in a table or a picture?

A table gives exact values. A chart shows a pattern at a glance: which group is larger, what is rising, where the cases are. Most theses need both, for different purposes.

Feature	Table	Chart (diagram or graph)
Best for	Exact values the reader will look up or recalculate	A pattern, trend or comparison seen at once
Amount	Many variables and subgroups together	One or two messages per figure
Precision	Numbers to the decimal place	Approximate. The eye reads sizes, not exact values
Risk	The pattern stays hidden in rows of numbers	Distortion from a poor scale, 3-D effects or the wrong chart type
In a thesis	Baseline characteristics and full results	Main findings, trends and the distribution of key outcomes

Do not present the same numbers twice, as a table and as a figure, unless each shows something the other does not.

Start here

Why plot the data before you summarise them?

Very different data can give identical summary numbers. Only a plot shows the difference.

Anscombe's four data sets (1973). Each has 11 points with mean x 9, mean y 7.50, variance of x 11, almost the same variance of y, correlation r = 0.816 and the same regression line, y = 3.00 + 0.500x (red). Only set I suits a straight-line summary. Set II is curved, one outlier tilts the line in set III, and in set IV a single point creates the whole relationship.

Tables

What makes a good table?

A reader should understand a table without reading the text around it.

Six parts of a good table. Keep one purpose per table, only the rows and columns you need, categories in a logical order (size, severity, age or time) and the same number of decimals throughout. The master chart of raw data belongs in the appendix, not in the results chapter.

A frequency distribution table lists how many observations fall in each category or class interval. Class intervals must not overlap (for example 2.0 to under 2.5 kg, then 2.5 to under 3.0 kg), and should be of equal width where possible.

Types of frequency table. A one-way table classifies subjects by one variable, a two-way (contingency) table cross-classifies them by two, and a multi-way table by three or more. Each box is a cell, and the count in it is the cell frequency. In a contingency table every subject appears in exactly one cell.

Questions that allow more than one answer. When a patient can report several symptoms, the percentages can add up to more than 100. Teaching example: of 120 patients, 96 (80%) had fever, 72 (60%) cough and 30 (25%) breathlessness, a total of 165%. Give the number of patients as the base, and add a footnote saying that more than one answer was allowed.

Which percentage? Calculate percentages in the direction in which the groups were chosen. In a case–control study, give the percentage exposed among cases and among controls. In a cohort study or a trial, give the percentage with the outcome in each exposure or treatment group.

Footnote symbols vary between journals. The ICMJE Recommendations mention letters or symbols such as *, †, ‡ and §, and tell authors to follow each journal's instructions.

Two types of data

Is your variable a category or a number?

The type of variable decides the chart. Categories are counted and shown as diagrams. Measurements lie on a number scale and are shown as graphs.

A discrete count with only a few values (number of children: 0, 1, 2, 3) can be drawn like categories, with a bar chart. Distribution shapes, mean and standard deviation are covered in Descriptive statistics.

Qualitative data

How do you compare categories?

With bars of equal width whose lengths are drawn to one scale that starts at zero.

One survey, three bar charts (made-up data: 100 rural and 100 urban girls). Simple bar: one variable (Mod. = moderate, Sev. = severe). Multiple bar: the same categories compared across groups, side by side. Component bar: each bar is one group divided into its parts. When the groups differ in size, draw the bars as 100% so the parts are percentages.

Keep bar widths equal and gaps equal. Only the length carries information.
Order nominal categories by size. Keep ordinal categories in their natural order.
Bars can be horizontal. This leaves room for long category names.

Qualitative data

Which bar charts have a special use?

Two bar charts appear often in community medicine and in hospital audits: the population pyramid and the Pareto chart.

Population pyramid (made-up district). Horizontal bars for each age group, men on the left and women on the right, youngest at the bottom. Each bar is a percentage of the whole population, so the two sides add up to 100%. A broad base means a large share of children, and a narrow top a small share of older people. Use equal age groups, except for the open last group.

Pareto chart (made-up audit of 200 medication errors). The bars are sorted from the most frequent type, with 'other' last, and a line shows the cumulative percentage on the right-hand axis. The three commonest types account for 70.5% of the errors, so the audit acts on them first.

Qualitative data

How do you show parts of a whole?

A pie chart divides a circle in proportion to each category's share. It works only when the parts add up to one whole.

Angle of a slice = (category count ÷ total) × 360°

No anaemia: 93 ÷ 200 × 360° = 167.4°

The four slices are 167.4°, 102.6°, 70.2° and 19.8°. People judge positions along a common scale more accurately than other visual features (Cleveland and McGill, 1984), so small differences are easier to see as bars than as slices. Use a pie for one group with a few categories. To compare groups, use bars.

Comparison

Histogram or bar chart: why do some bars touch?

A bar chart counts separate categories. A histogram divides one continuous scale into class intervals, so the bars sit next to each other.

Made-up data: blood group of 120 donors, and birth weight of 120 newborns in half-kilogram class intervals.

Feature	Bar chart	Histogram
Data	Categories or a few discrete values: blood group, anaemia grade	Continuous: birth weight, haemoglobin, age
Horizontal axis	Categories. Nominal ones can be reordered	A number scale divided into class intervals, in fixed order
Gaps	Equal gaps between bars	No gaps. Neighbouring intervals share a boundary
Frequency is shown by	Length of the bar	Area of the bar. With equal intervals, height also works
Unequal intervals	Not applicable	Height = frequency ÷ interval width (frequency density)
Example	44 donors with blood group O	38 newborns from 2.5 kg to under 3.0 kg

Frequency density = frequency ÷ width of the class interval

In the histogram, the interval from 2.5 to under 3.0 kg has 38 babies: 38 ÷ 0.5 kg = 76 per kg. If you merged the last two intervals (3.5 to 4.5 kg, 17 + 5 = 22 babies), the merged bar must be drawn at 22 ÷ 1.0 kg = 22 per kg. Drawing it at the height of a half-kilogram class would double its area.

Interactive

Change the class width and merge intervals, and watch the histogram change

Try this: merge the last two intervals, then switch the bar height between frequency and frequency density. Watch the area of the merged bar. Then try class widths of 0.1 kg and 1.0 kg.

Teaching example (made-up data): birth weights of the 120 newborns from the district hospital histogram above, recorded to the gram.

4.2%of the bar area is in the last bar, which holds 4.2% of the babies

6 intervals · last interval 4.0 to under 4.5 kg: 5 babies ÷ 0.5 kg = 10 per kg

All intervals are 0.5 kg wide, so frequency and frequency density give the same shape. Only the scale on the vertical axis changes. With 0.5 kg intervals, the fullest interval holds 38 babies, and 0 of 6 intervals hold 2 babies or fewer.

Quantitative data

How do you show the shape and still keep every value?

A stem-and-leaf plot splits each value into a stem (the leading digits) and a leaf (the last digit).

Haemoglobin of 30 women (made-up data). Each leaf is one woman. The values can be read back exactly, and the lengths of the rows show the shape of the distribution. Two groups can be compared with a back-to-back plot, which shares the stems and puts one group's leaves on each side.

A dot plot draws one dot per value along a scale and stacks equal values. Both plots suit small samples, where a histogram with few values in each bar changes shape with the choice of class width.

Quantitative data

How do you compare two distributions on one graph?

Join the midpoints of the tops of the histogram bars. Lines take less space than bars, so two or more groups fit on one graph.

District hospitalMedical college hospital

Birth weight of 120 newborns in each of two hospitals (made-up data). The grey bars are the district hospital histogram. Each polygon is closed on the baseline at the midpoints of the empty intervals at either end. Babies under 2.5 kg: 24 of 120 in the district hospital, 13 of 120 in the medical college hospital.

A cumulative frequency curve (ogive) plots the running total of observations up to the upper limit of each interval. The median and percentiles can be read from it.

With a very large number of observations and very narrow classes, the polygon becomes a smooth frequency curve, the kind of shape drawn for the normal distribution.

Quantitative data

How do you read the median and percentiles from a graph?

Plot the cumulative percentage against the upper limit of each class, join the points, and read across.

District hospital birth weights from the histogram above (made-up data): 6, 24, 62, 98, 115 and 120 babies weighed less than 2.0, 2.5, 3.0, 3.5, 4.0 and 4.5 kg. Read across at 50% for the median and at 25% and 75% for the quartiles.

Median = 2.5 + [(60 − 24) ÷ 38] × 0.5 = 2.97 kg

Joining the points with straight lines gives the same values as the grouped-data formula in Descriptive statistics: the 60th of 120 babies lies in the class 2.5 to under 3.0 kg, which starts after 24 babies and holds 38.

Quantitative data

How do you show change over time?

Put time on the horizontal axis and the measurement on the vertical axis, and join the points in time order.

Dengue cases per month in one district (made-up data). The reader judges the slope and position of the line, not the length of a bar, so a line graph may start its vertical axis above zero if the axis is labelled clearly. Space time points to scale: readings at 0, 2, 6, 12 and 24 hours need unequal gaps on the axis.

Separate lines for two groups on one graph show whether the groups change in the same way. Lines that are not parallel suggest that the effect of one factor depends on the other, an interaction, covered in Two-way ANOVA and interaction.

Quantitative data

When should an axis be logarithmic?

On a logarithmic axis equal distances stand for equal ratios, so growth by a fixed percentage appears as a straight line.

Made-up outbreak: cases double every 3 days, from 5 to 640. On the ordinary axis the first two weeks look flat. On the logarithmic axis each doubling takes the same vertical distance, so the line is straight, and a change in the rate of growth would show as a bend.

Use a logarithmic axis when values cover several powers of ten, such as viral load, antibody titres or bacterial counts, or when relative change is the message. Say that the axis is logarithmic, label the ticks with the actual values (1, 10, 100, 1,000), and remember that zero cannot be shown on it.

Quantitative data

Do two measurements rise and fall together?

Plot one dot per patient, with one measurement on each axis.

Body mass index and systolic BP in 30 adults (made-up data). The dots rise from lower left to upper right: a positive relationship, Pearson r = 0.78. A scatter plot shows that two measurements vary together. It does not show that one causes the other. Measuring the relationship is covered in Correlation and regression.

When many points overlap, as with whole-number scores, add a small random shift to each point (jitter) or use smaller symbols. Different symbols can mark different groups. A bubble chart adds a third variable as the area of each circle. In regression, a scatter plot of the residuals against the fitted values is used to check the model, covered in Multiple linear regression.

Quantitative data

How do you show the middle, the spread and the outliers?

A box plot summarises a measurement with five values and draws the unusual values separately.

Days in hospital after surgery, 21 patients per ward (made-up data). The box runs from the lower quartile (Q1) to the upper quartile (Q3), so it holds the middle half of the patients. The red line is the median. Whiskers reach the most extreme values within 1.5 × IQR of the box, and values beyond that are drawn as separate points (outliers). Ward B stays longer and varies more.

IQR = Q3 − Q1 = 7 − 4 = 3 days

Upper limit = Q3 + 1.5 × IQR = 7 + 4.5 = 11.5 days → 18 days is an outlier

Outer limit = Q3 + 3 × IQR = 7 + 9 = 16 days → 18 days lies beyond this limit too

Some programs mark values beyond 1.5 × IQR as outliers and values beyond 3 × IQR as extreme outliers, with different symbols. A box plot also shows skew: when the median lies near one end of the box and one whisker is longer, the data are skewed towards the longer whisker. Programs calculate quartiles in slightly different ways, so small differences between them are expected.

Diagrams for the public

How do you show numbers to patients and the community?

With identical symbols that each stand for a fixed number, or with a spot map of where the cases occurred.

Pictogram (made-up data): count the figures and multiply by the key. An icon array shows a risk as people out of a round total, here 4 in 20 (20%). Pictograms suit posters and health education material for readers who find numbers and axes hard to follow. They give approximate values only, and parts of a symbol are hard to read.

Spot map (made-up data): one dot per case at its address, with the possible sources marked. 32 of the 36 cases lie within one block of pump 2, so pump 2 is the first source to investigate. A spot map shows where cases are, not how many people live there. A crowded area can have more cases without a higher risk.

Diagrams in medicine

Which diagrams are special to medicine and public health?

Several diagrams are built for one clinical or public health purpose. Each is a bar chart, a line graph or a map with a fixed layout.

Epidemic curve

Cases by day of onset (made-up data), drawn as touching bars. In CDC's description, a point-source outbreak gives a curve with a steep upslope and a more gradual downslope, with most cases within one incubation period. Person-to-person (propagated) spread gives progressively taller peaks about one incubation period apart. The incubation period here is about 5 days.

Spot map or choropleth map?

Feature	Spot map	Choropleth map
Shows	Each case at its location	A rate for each area, shaded by class
Needs	The address of every case	Cases and the population of every area
Answers	Where do cases cluster?	Which areas have the highest rate?
Caution	Crowded areas have more dots without a higher risk	The classes in the key change the picture, and large areas look important even when few people live there

Choropleth map (made-up data). Block H has the highest rate, 6.0 per 1,000. Block I has more cases than blocks A, C, F and G, but a low rate, because 15,000 people live there. State the classes used for the shading.

Charts used in patient care and in the laboratory

Growth chart: line graphs of percentile or z-score curves for weight, height or head circumference by age, from a reference population. A child's own measurements, joined over time, show whether growth follows a percentile curve or crosses them. Percentiles are explained in Descriptive statistics.
Partograph: a chart of the progress of labour with an alert line and an action line. In a WHO multicentre trial in South East Asia involving 35,484 women, introducing the partograph with an agreed labour-management protocol reduced prolonged labour from 6.4% to 3.4% of labours (WHO, 1994).
Control chart: a line graph of repeated results on control material with limits drawn at set numbers of SDs from the mean, covered in Laboratory quality control and reference intervals.
Nomogram: scaled lines from which a result is read with a ruler instead of a calculation. Fagan (1975) published one for Bayes' theorem, which gives the probability of disease after a test result from its likelihood ratio. See Bayes' rule and combining tests.
Covered in other chapters: the Kaplan–Meier curve (risk and survival), the ROC curve (diagnostic tests), forest and funnel plots (systematic reviews), and the CONSORT flow diagram below.

Clinical trials

How do you show what happened to every patient in a trial?

With a CONSORT flow diagram. It follows the patients from screening to analysis, with numbers and reasons at every step.

Made-up numbers in the CONSORT 2025 template, which has four stages: enrolment, allocation, follow-up and analysis. Check the arithmetic: 240 − 60 = 180 randomised, 90 + 90 = 180 allocated, 90 − 4 = 86 and 90 − 6 = 84 analysed. In a real report, each box also gives the reasons.

The diagram tells the reader how many patients were lost, from which group and why. Unequal losses between groups can bias the result: see Bias and validity. Trial design itself is covered in Clinical trials.

Decide

Which chart fits your data?

Answer one or two questions about your data and your message. Each answer links back to its picture.

What do you want the reader to see?

Which chart: all possible answers

Simple bar chart: One bar per category, equal widths, gaps between bars, axis starting at zero.
Pie chart: Angle of each slice = its share × 360°. Keep it flat and use it for a few categories only.
Multiple bar chart: Bars for each group placed side by side within each category, with a legend.
Component bar chart: One bar per group, divided into segments. A 100% component bar compares percentages when group sizes differ.
Pictogram: Rows of identical symbols, each standing for a stated number. Never enlarge a symbol to show a larger number.
Histogram: Class intervals on a continuous scale, bars touching, area of each bar proportional to its frequency.
Frequency polygon: Join the midpoints of the class intervals. Several polygons fit on one graph where histograms would overlap.
Box plot: Median, quartiles, whiskers and outliers for each group, drawn on one shared scale.
Dot plot (univariate scatter plot): One dot per patient in each group, with the median or mean marked. A bar of the mean hides how the values are spread.
Line graph: Time on the horizontal axis at equal intervals, the measurement on the vertical axis, points joined in order.
Scatter plot: One dot per patient, one measurement on each axis. Then quantify the relationship with correlation or regression.
Spot map: One dot per case at its location, with the possible sources (wells, pumps, factories) marked.
CONSORT flow diagram: Boxes for enrolment, allocation, follow-up and analysis, with numbers and reasons at every step.
Table: Numbered, titled, with column headings and units, totals, footnotes and the source.
Population pyramid: Horizontal bars for each age group, men on one side and women on the other, youngest at the bottom.
Epidemic curve: Cases by date of onset as touching bars. The shape suggests a point source or person-to-person spread.
Choropleth map: Each area shaded by its rate, with the classes stated in a key. Rates need the population of every area.
Stem-and-leaf plot: Leading digits as stems, the last digit of each value as a leaf. The shape shows, and every value can be read back.
Cumulative frequency curve (ogive): Cumulative percentage against the upper limit of each class. Read across at 25%, 50% and 75%.

Illustrations

What makes an illustration clear and honest?

A reader should understand the figure from the figure and its legend alone, and every size in the picture should be in proportion to its number.

Methods of illustration in a thesis or paper: tables, charts and graphs, line drawings and diagrams (flow charts, schematic drawings), photographs and clinical images, photomicrographs, and maps.

Number figures in the order they are cited. Write a legend that says what is shown, in whom, where and when.
Label both axes with the variable and its unit. State n.
Start the axis of a bar chart at zero, so that bar length is proportional to the value.
Keep scales honest: time to scale, equal class widths, the same scale when panels are compared.
Use flat charts. 3-D effects change the angles and areas that carry the numbers.
One message per figure. Remove grid lines, shading and decoration that carry no data.
Make letters and symbols large enough to read when the figure is reduced.
Say what error bars show: SD, SE or 95% confidence interval.
In a small study, show each value, not only a bar of the mean.
Use shades or patterns that still work when printed in black and white.
For photographs: the same lighting for before-and-after images, a scale marker on photomicrographs, and the patient's consent.

Common errors

How can a graph mislead?

Most misleading graphs draw a correct number at the wrong size. Here are four common errors, each shown before and after correction.

1. The axis does not start at zero

Made-up means: rural 11.0 g/dL, urban 11.5 g/dL. With the axis starting at 10.8, the bars are 0.2 and 0.7 units tall, so the urban bar is drawn 3.5 times as long for a 4.5% difference.

Lie factor = size of the effect shown in the graphic ÷ size of the effect in the data

Data: (11.5 − 11.0) ÷ 11.0 = 4.55% difference
Graphic: (0.7 − 0.2) ÷ 0.2 = 250% difference in bar length

Lie factor = 250 ÷ 4.545 = 55.0

Edward Tufte defined the lie factor in 1983. A value of 1 means the graphic shows the effect at its true size.

2. A 3-D pie

Four equal slices. Tilting the pie squeezes the side wedges to 44° and widens the front and back wedges to 136°. The front slice also gains a side wall: in this drawing it covers 36% of the coloured area, the back slice 19%.

3. A symbol enlarged to show a larger number

Doubling both the height and the width of a symbol multiplies its area by four. Readers judge the area, so 80 looks four times as large as 40.

4. A bar of the mean hides the values

Made-up data, 12 patients per group. The bars (means 50 and 49.5) look alike, but group B has nine low values and three high ones, with a median of 43.5. In a review of 703 physiology papers, most showed continuous data only as bar or line graphs, and the authors recommended showing the individual values in small studies (Weissgerber and colleagues, 2015).

5. A line graph stretched or squashed

Made-up clinic means: HbA1c fell from 8.4% to 8.0% over 6 months, a fall of 0.4 percentage points (4.8%). A narrow axis range makes the fall look large, and a wide range hides it. Choose the range from the size of change that matters clinically, label it, and use the same range for graphs that will be compared.

Other common errors: unequal time intervals drawn as equal, two vertical axes with different scales on one graph, and percentages shown without the number of patients.

Interactive

Move the start of the vertical axis and watch the lie factor change

Try this: move the start of the vertical axis from 0 to 10.8 and watch the lie factor rise from 1.0 to 55.0.

The chapter's made-up means: mean haemoglobin 11.0 g/dL in rural girls and 11.5 g/dL in urban girls.

Vertical axis starts at0.0 g/dL

Closer to the data → the difference looks larger

1.0lie factor

data: (11.5 − 11.0) ÷ 11.0 = 4.55% · graphic: (11.5 − 11.0) ÷ 11.0 = 4.55% · lie factor = 4.55% ÷ 4.55% = 1.0

The urban bar is drawn 1.05 times as long as the rural bar, but urban haemoglobin is only 4.55% higher. With the axis at zero, the lie factor is 1: the graphic shows the difference at its true size.

A bar chart shows a value by the length of its bar, so its axis starts at zero.

By specialty

Presenting data by specialty

Dengue cases in a town during an outbreak, with the addresses of every case and the location of water storage sites.

A spot map shows where cases cluster. A line graph of cases per week shows when the outbreak peaked.

Common myths

Common mistaken beliefs

Myth: A pie chart suits any categorical data.
Only when the categories are parts of one whole. To compare groups or small differences, use bars.
Myth: A histogram is a bar chart with the gaps removed.
A histogram is drawn on a continuous scale, and the area of each bar shows the frequency. Unequal class widths change the heights.
Myth: 3-D charts look more professional.
Tilt and depth distort angles and areas. In the example above, four equal slices are drawn as 136° and 44° wedges.
Myth: The vertical axis can start wherever the data start.
Not for bars, whose length shows the value. The axis of a bar chart starts at zero.
Myth: A bar of the mean ± SE shows my results.
Very different sets of values can give the same bar. In a small study, show each value (Weissgerber and colleagues, 2015).
Myth: John Snow found the Broad Street pump by drawing his map.
Snow did not write that he used a map to identify the source. His map, published in 1855, illustrated his argument, and deaths were already falling before the pump handle was removed (McLeod, 2000).

Why this matters to you

Five consequences of presenting data badly

Corrections to the thesis
Examiners return figures with unlabelled axes, missing units, no n, or 3-D charts.
A question you cannot answer at the viva
"Why is anaemia grade drawn as a histogram?" Categories need a bar chart.
A small difference shown as a large one
A bar chart with a truncated axis overstates the effect, and examiners check the axis.
Revision requests from journals
Journals expect numbered, titled tables, self-explanatory figures and, for randomised trials, a flow diagram.
Misreading papers
A bar of the mean can hide a result driven by a few extreme patients.

History

History of statistical charts

1786
William Playfair
Published The Commercial and Political Atlas, the first book to contain statistical charts. It included line graphs of England's trade over time and a bar chart of Scotland's imports and exports.
1801
William Playfair
His Statistical Breviary introduced the pie chart, in a chart comparing the areas and populations of countries.
1855
John Snow
The second edition of On the Mode of Communication of Cholera included his map of cholera deaths in the Golden Square area of London from 19 August to 30 September 1854, with the water pumps marked.
1858
Florence Nightingale
Her Notes on Matters Affecting the Health, Efficiency and Hospital Administration of the British Army included polar area diagrams, also called rose or coxcomb diagrams, of the causes of death in the army in the East.
1891
Karl Pearson
Used the word "histogram" in his lectures at Gresham College, London. In print in 1895 he described it as "columns marking as areas the frequency corresponding to the range of their base".
1973
F.J. Anscombe
Published four small data sets with the same means, variances, correlation and regression line but very different scatter plots, to show that data should be plotted before they are summarised.
1978
McGill, Tukey and Larsen
Described the box plot as a display of five values (the extremes, the upper and lower hinges, and the median) and three variants, one showing group size and one indicating whether medians differ.
1983
Edward Tufte
The Visual Display of Quantitative Information defined the lie factor: the size of an effect shown in a graphic divided by its size in the data.
1984
William Cleveland and Robert McGill
Ranked the visual tasks people perform when reading graphs by how accurately they are done. Judging position along a common scale was the most accurate.
2015
Weissgerber and colleagues
Reviewed 703 papers in physiology journals. 85.6% included at least one bar graph, and scatter plots, box plots and histograms were rare. They recommended showing individual values in small studies.
2025
CONSORT 2025
A 30-item checklist and a flow diagram of participants through enrolment, allocation, follow-up and analysis. It replaced CONSORT 2010.

Guidelines

Tables, figures and flow diagrams in guidelines

ICMJE Recommendations: Tables

“Number tables consecutively in the order of their first citation in the text and supply a title for each.” Authors should “place explanatory matter in footnotes, not in the heading” and “identify statistical measures of variations, such as standard deviation and standard error of the mean.”

ICMJE Recommendations: Illustrations (Figures)

Letters, numbers and symbols should be “large enough to remain legible when the figure is reduced for publication.” Figures should be “as self-explanatory as possible”, and titles and detailed explanations belong in the legends, not on the illustrations. A previously published figure needs acknowledgement and written permission.

CONSORT 2025 (BMJ 2025;389:e081123)

The statement consists of “a 30-item checklist of essential items” and “a diagram for documenting the flow of participants through the trial.” Its template boxes include “Lost to follow-up for primary outcome” and “Analysed for primary outcome”.

Steps

Making a chart, step by step

Write down the one message the figure must show.
Identify the variable type (category or number) and the purpose (comparison, share, distribution, trend, relationship or location).
Choose the chart with the decision tree above.
Set the scales: bars from zero, time to scale, the same scale across panels.
Label the axes with units, and add n, a key and the source.
Remove 3-D effects, shading and decoration that carry no data.
Number the figure and write a legend that explains it without the text.
Check it in black and white and at the size it will be printed.

Reading a paper

Five checks on any paper's tables and figures

Does each axis have a label, a unit and a scale, and does every bar chart start at zero?
Does the chart type match the data: bars for categories, a histogram for a continuous measurement?
Are n and the meaning of any error bar (SD, SE or confidence interval) stated?
In a small study, can you see the individual values, or only a bar of the mean?
In a trial, does the flow diagram account for every patient screened and randomised?

Why is it called that?

Word surgery

“Frequency”

In everyday speech

How often something happens in a period, as in frequency of urination, or a radio frequency.

In research

The number of observations in a category or class interval. A frequency distribution lists these counts.

“Graph”

In everyday speech

Any chart or picture of numbers.

In research

In this chapter, a drawing on a numeric scale: histogram, frequency polygon, line graph, scatter plot, box plot. Bar charts, pie charts, pictograms and maps are called diagrams.

Memory trick

Gaps between bars: separate categories. Bars touching: one continuous scale.

Diagram

Greek diagramma: "that which is marked out by lines"

From dia- "across, through" and graphein "to write, mark, draw". A drawing that gives the outline or scheme of something.

Graph

English, 1878: a shortening of "graphic formula"

A drawing of numbers on a scale.

Histogram

histo- + -gram, recorded from 1891. Greek histos: "web", literally "anything set upright". Greek gramma: "that which is drawn"

Karl Pearson used the word in his 1891 Gresham lectures for columns whose areas show frequencies.

Polygon

Greek polygōnos: "many-angled"

The frequency polygon is the many-angled line that joins the midpoints of the class intervals.

Pictogram

Latin pictus: "painted" + -graph: "something written"

A chart of picture symbols, each standing for a fixed number. The form pictograph is recorded from 1851.

Statistics

German Statistik, from Latin status: "position, condition"

It first meant data about the condition of a state. The meaning "numerical data of any sort collected and classified systematically" is recorded from 1829.

Exam answers

Model answer outlines

Presentation of data (data presentation)

Ph.D. RM 2014, 2015, 2023 · MD Community Medicine 2011

Aim: make data understandable at a glance, show patterns and comparisons, and save space in the text.
Methods: tabular, diagrammatic and graphic presentation, with text for a few key numbers.
Tables: simple and complex (cross-tabulation) tables, frequency distribution tables. Parts: number, title, column headings with units, row labels in logical order, totals, footnotes, source.
Diagrams for qualitative and discrete data: simple, multiple and component bar charts, pie chart, pictogram, spot map. Also the population pyramid, the Pareto chart and the choropleth map.
Graphs for quantitative data: histogram, frequency polygon, cumulative frequency curve (ogive), line graph, scatter plot, box plot. Also the stem-and-leaf plot and the dot plot.
Diagrams special to health: epidemic curve, growth chart, partograph, laboratory control chart, nomogram, Kaplan–Meier curve.
Plot the data first: identical summary statistics can hide very different data (Anscombe, 1973).
Flow diagrams: the CONSORT flow diagram for randomised trials.
Principles: self-explanatory title, labelled axes with units, n stated, bar charts from zero, time to scale, no 3-D effects, source given.
Choice: by type of data and purpose (see the decision tree and the table in the next answer).

Effective presentation of data through diagrams and graphs (diagrammatic representation)

Ph.D. RM 2018 · MD Community Medicine 2017

Chart	Data	Shows	Caution
Simple bar	Categories	Counts or percentages	Axis from zero, equal widths
Multiple bar	Categories in two or more groups	Each category across groups	Legend needed
Component bar	Categories in two or more groups	Make-up of each group	Use 100% bars if totals differ
Pie chart	Parts of one whole	Share of the total	Few slices, flat, no 3-D
Pictogram	Counts	Numbers for the public	Same-size symbols with a key
Spot map	Locations of cases	Clustering	No population at risk shown
Histogram	Continuous	Shape of the distribution	No gaps, area = frequency
Frequency polygon	Continuous	Two or more distributions	Close on the baseline
Line graph	Measurement over time	Trend	Time to scale
Scatter plot	Two measurements	Relationship	Does not show cause
Box plot	Continuous, often skewed	Median, IQR, outliers	Explain the whiskers
Stem-and-leaf plot	Continuous, small sample	Shape, with every value	Give a key (9 \| 3 = 9.3)
Ogive	Continuous, grouped	Median and percentiles	Plot at the upper class limits
Population pyramid	Age groups by sex	Population structure	Equal age groups
Pareto chart	Categories of a problem	Commonest causes and their cumulative share	Sort the bars, ‘other’ last
Epidemic curve	Cases by date of onset	Course of an outbreak	Bars touch, sensible time unit
Choropleth map	Rates by area	Geographical variation	Needs populations, state the classes

Effective when: one message per figure, axes labelled with units, n stated, scales in proportion to the numbers, and a legend that stands on its own.

Methods of illustration, and how to make an effective illustration

Ph.D. RM 2017 (January and July)

Methods:

Tables.
Charts and graphs (bar, pie, histogram, line, scatter, box plot).
Line drawings and diagrams: flow charts, schematic drawings, flow diagrams of participants.
Photographs and clinical images: radiographs, specimens, operative photographs.
Photomicrographs, with internal scale markers and the stain named.
Maps.
Diagrams special to medicine: epidemic curve, growth chart, partograph, control chart, nomogram.

Making it effective:

Decide the message, then choose the type of illustration by the data.
Number figures in the order of citation. Put titles and explanations in the legend, not on the figure (ICMJE).
Letters and symbols legible when reduced. Figures as self-explanatory as possible (ICMJE).
Honest scales: bars from zero, no 3-D, no enlarged symbols. The lie factor should be close to 1 (Tufte).
State n and what error bars show. In small samples, show individual values.
Before-and-after photographs with the same lighting. Consent for clinical photographs.
Acknowledge and get permission for previously published figures.

CONSORT diagram

DM Medical Oncology 2017

Definition: the flow diagram of the CONSORT (Consolidated Standards of Reporting Trials) statement, showing the progress of participants through a randomised trial.
Current version: CONSORT 2025 (Hopewell and colleagues, BMJ 2025;389:e081123): a 30-item checklist and a flow diagram. It replaced CONSORT 2010.
Enrolment: assessed for eligibility, excluded (not meeting inclusion criteria, declined to participate, other reasons), randomised.
Allocation (each group): allocated to intervention, received allocated intervention, did not receive it (with reasons).
Follow-up: lost to follow-up for primary outcome (with reasons), discontinued intervention (with reasons).
Analysis: analysed for primary outcome, excluded from analysis (with reasons).
Uses: shows how many were lost and whether losses differ between groups, shows who was analysed, and helps readers judge attrition bias and to whom the result applies.
Draw an example: 240 assessed, 60 excluded, 180 randomised, 90 per group, 86 and 84 analysed.

Use of pictograms in health education

MD Community Medicine 2002

Pictogram: a diagram in which a picture symbol stands for a fixed number of units, explained in a key.
Forms: rows of repeated symbols (each figure = 10 immunised children), and icon arrays that show a risk as people out of a round total (4 in 20 adults).
Uses: posters and information, education and communication (IEC) material, explaining risk to patients, comparing coverage between villages or years, and reaching readers with limited literacy or numeracy.
Rules: identical symbols of one size, a stated key, round numbers, familiar symbols, a title and the source.
Limitations: approximate values only, parts of symbols are hard to read, and enlarging a symbol exaggerates the number.

The same question also asked about non-parametric tests: see Choosing a test.

The one thing to remember

Choose the chart from the type of data and the message, label every axis with its unit, and draw every number to scale.

All data in the figures and worked examples are made up for teaching. Numbers were computed in Python.

Sources: Playfair W. The Commercial and Political Atlas. London; 1786, and The Statistical Breviary. London; 1801. Symanzik J, Fischetti W, Spence I. Commemorating William Playfair's 250th birthday. Comput Stat 2009;24:551–66 (doi:10.1007/s00180-009-0170-z). McLeod KS. Our sense of Snow: the myth of John Snow in medical geography. Soc Sci Med 2000;50:923–35 (doi:10.1016/s0277-9536(99)00345-7). Shiode N et al. Int J Health Geogr 2015;14:21 (doi:10.1186/s12942-015-0011-y). Nightingale F. Notes on Matters Affecting the Health, Efficiency and Hospital Administration of the British Army. London: Harrison and Sons; 1858. McDonald L. Florence Nightingale, statistics and the Crimean War. J R Stat Soc A 2014;177:569–86 (doi:10.1111/rssa.12026). Pearson K. Contributions to the mathematical theory of evolution. II. Skew variation in homogeneous material. Phil Trans R Soc Lond A 1895;186 (footnote, p. 399; doi:10.1098/rsta.1895.0010). McGill R, Tukey JW, Larsen WA. Variations of box plots. Am Stat 1978;32:12–16 (doi:10.1080/00031305.1978.10479236). Tufte ER. The Visual Display of Quantitative Information. Cheshire, CT: Graphics Press; 1983. Cleveland WS, McGill R. Graphical perception. J Am Stat Assoc 1984;79:531–54 (doi:10.1080/01621459.1984.10478080). Weissgerber TL et al. Beyond bar and line graphs. PLoS Biol 2015;13:e1002128 (doi:10.1371/journal.pbio.1002128, PMID 25901488). Hopewell S et al. CONSORT 2025 statement. BMJ 2025;389:e081123 (PMID 40228833). International Committee of Medical Journal Editors. Recommendations: Preparing for Submission, sections on tables and illustrations (icmje.org).

Added sources: Anscombe FJ. Graphs in statistical analysis. Am Stat 1973;27:17–21 (doi:10.1080/00031305.1973.10478966). Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice, 3rd ed., Lesson 1, section 11 (epidemic curves). World Health Organization Maternal Health and Safe Motherhood Programme. World Health Organization partograph in management of labour. Lancet 1994;343:1399–404 (PMID 7910888). Fagan TJ. Nomogram for Bayes's theorem. N Engl J Med 1975;293:257 (doi:10.1056/NEJM197507312930513; PMID 1143310).

Past papers

Every TNMGRMU question on presenting data

Each one is answered in this chapter. Tap a sitting to open the university's own question paper.

×3Data presentationPh.D. RM · Jan 2023 Ph.D. RM · Jan 2015 MD Community Medicine · Oct 2011
×1Describe the effective presentation of data through diagrams and graphsPh.D. RM · Jul 2018
×1Diagrammatic representation of dataMD Community Medicine · May 2017
×1CONSORT diagramDM Medical Oncology · Feb 2017
×1Methods of illustrationsPh.D. RM · Jan 2017
×1How do you make an effective illustration?Ph.D. RM · Jul 2017
×1Presentation of dataPh.D. RM · Jul 2014
×1Non parametric tests. (bh) Use of pictograma in health education. ic} Communication barriers. fe) Multidrug resistant tuberculosisMD Community Medicine · Mar 2002

Should the numbers go in a table or a picture?

Why plot the data before you summarise them?

What makes a good table?

Is your variable a category or a number?

How do you compare categories?

Which bar charts have a special use?

How do you show parts of a whole?

Histogram or bar chart: why do some bars touch?

Change the class width and merge intervals, and watch the histogram change

How do you show the shape and still keep every value?

How do you compare two distributions on one graph?

How do you read the median and percentiles from a graph?

How do you show change over time?

When should an axis be logarithmic?

Do two measurements rise and fall together?

How do you show the middle, the spread and the outliers?

How do you show numbers to patients and the community?

Which diagrams are special to medicine and public health?

Epidemic curve

Spot map or choropleth map?

Charts used in patient care and in the laboratory

How do you show what happened to every patient in a trial?

Which chart fits your data?

Choose a chart for each data set and see whether it fits

What makes an illustration clear and honest?

How can a graph mislead?

1. The axis does not start at zero

2. A 3-D pie

3. A symbol enlarged to show a larger number

4. A bar of the mean hides the values

5. A line graph stretched or squashed

Move the start of the vertical axis and watch the lie factor change

Presenting data by specialty

Common mistaken beliefs

Five consequences of presenting data badly

Corrections to the thesis

A question you cannot answer at the viva

A small difference shown as a large one

Revision requests from journals

Misreading papers

History of statistical charts

William Playfair

William Playfair

John Snow

Florence Nightingale

Karl Pearson

F.J. Anscombe

McGill, Tukey and Larsen

Edward Tufte

William Cleveland and Robert McGill

Weissgerber and colleagues

CONSORT 2025

Tables, figures and flow diagrams in guidelines

Making a chart, step by step

Five checks on any paper's tables and figures

Word surgery

“Frequency”

“Graph”

Diagram

Graph

Histogram

Polygon

Pictogram

Statistics

Model answer outlines

Presentation of data (data presentation)

Effective presentation of data through diagrams and graphs (diagrammatic representation)

Methods of illustration, and how to make an effective illustration

CONSORT diagram

Use of pictograms in health education

Every TNMGRMU question on presenting data

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