This document discusses the history and effective use of graphical representations of data. It covers the origins of graphical displays in the 18th century work of William Playfair and how graphics can both report and reveal patterns in data. The document provides examples of different types of graphs like line graphs, scatter plots, and maps and discusses how to design graphs for integrity and avoid misrepresentation. Guidelines are given for clearly labeling and interpreting graphics used in documents.

1.  English 317: Technical Writing
Graphically Representing Data
The following slides were prepared from the first chapter of
Edward Tufte’s, The Visual Display of Quantitative Information.
1

2. History of graphically representing quantitative data.
 Visually representing numbers is a new invention.
 It was not until 1750-1800 that statistical graphics were
invented.
 William Playfair (1759-1823) developed almost all of the
fundamental graphical designs, replacing the conventional
tables of numbers with visual representations.
2

3. This is Playfair’s chart comparing the price of wheat/bread to wages paid to
smiths, masons, and carpenters between 1565 to 1821.
3

4. Playfair’s interpretation of his data:
never before at any period was wheat so cheap in
proportion to mechanical labor
The graphic depicted wages paid to mechanical labor; he did
not collect data on wages paid to non-mechanical labor –
those working in factories under terrible conditions.
Graphics both report data and reveal it. The graphics are only
as effective as the data used to derive them.
4

5. The statistician F.J. Anscombe demonstrated why it is important to graph data before
analyzing it. The quartet consists of four sets of data that have identical simple
statistical properties. They are, however, very different when graphed.
Anscombe’s quartet shows how graphics do not just report data, they reveal data.
Therefore, they are instruments for reasoning about quantitative information.
5

6. One of the earliest uses of a map to
chart patterns (data map) was done
by Dr. John Snow. He plotted the
location of deaths from cholera in
London for September in 1854.
By analyzing the scatter of dots
(which marked deaths), Snow
observed that cholera occurred
almost exclusively among those who
lived near (and drank from) the
Broad Street water pump (circled on
this map).
He ended the epidemic that had
killed over 500 people by identifying
the source of contamination.
6

7. Example of a modern data map.
7

8. Data maps help us identify leads to causes but have their flaws.
 The flaws inherent to data maps such as the cancer map is that they
equate the visual importance of each county with its geographic area
rather than with the number of people living in the county.
 Our visual impression of the data is entangled with the circumstances of
geographic boundaries, shapes, and areas.
 An additional shortcoming of the cancer map is that it was created using
death certificate reports on the cause of death. These reports fall under
the influence of diagnostic fashion prevailing among doctors and coroners
in particular places and times.
 It’s not that data maps are not useful, it is just that you need to be careful
when interpreting what they mean.
8

9. Relational Graphics
 Link at least two variables.
 Encourage the viewer to assess the possible causal
relationship between the plotted variables.
 It displays causal theories that X causes Y with empirical
evidence as to the exact relationship between X and Y.
9

10. Relational graphics did not to appear in scientific writings
until the late 1700s.
Here is a drawing by Johann Heinrich Lambert. It shows the periodic
variation in soil temperature in relation to the depth under the
surface.
10

11. Relational graphics evolved to include multiple variables.
 The following slides shows the graphic, Charles Joseph Minard (1781-1870)
shows the losses suffered in 1812 by Napoleon’s army in Russia.
 Six variables are plotted 1) size of the army, 2) location of the army), 3) it’s
location on a two-dimensional surface, 4) the direction of the army’s
movement when advancing, 5) the direction of the army’s movement in
retreat, and 6) temperature on various dates during the retreat from
Moscow.
 The take-away when looking at the following graphic is to realize that
graphics can convey a high level of complexity if handled right.
11

12. Narrative graphic of Napoleon’s army invading Russia in 1812.
12

13. Tables can present words as well as numbers.
Date Time Power Level Event
April 25 1:00 a.m. 3200 MW Operators begin power descent
April 25 2:00 p.m. 1600 MW Power descent delayed for 9 hours
Emergency core-cooling system disconnected
April 25 11:10 p.m. 1600 MW Operators switch off automatic control
Power descent resumed
April 26 1:00 a.m. 30 MW Power minimum reached
April 26 1:19 a.m. 200 MW Operators pull rods beyond allowable limits
Operators start two additional coolant pumps
Operators violate coolant flow limits
April 26 1:23 a.m. 2,000,000 MW Power surges by factor of 10,000 in 5 seconds
Table 1. Sequence of events in the Chernobyl accident
13

14. Notice how the line graph more effectively conveys the story about glucose
levels in diabetics compared to those without diabetes.
300 Breakfast
Lunch Dinner
Table 2. [Carlson, 1982].
Blood glucose levels 250
Diabetic
Time Normal Diabetic Blood 200
(hour) (mg/dl*) (mg/dl) Glucose
Level
midnight 100.3 175.8 150
(mg/dl)
2:00 93.6 165.7
4:00 88.2 159.4 100
6:00 100.5 72.1
8:00 138.6 271.0 Non Diabetic
10:00 102.4 224.6 50
noon 93.8 161.8
2:00 132.3 242.7
4:00 103.8 219.4 0
6:00 93.6 152.6 12:00 pm 6:00 am 12:00 6:00pm 12:00 am
8:00 127.8 227.1
10:00 109.2 221.3 Hour
* decaliters/milligram Figure 11. Blood glucose levels for diabetic compared to
individuals who do not have the disease. [Carlson, 1982].
14

15. Pie Charts
 Show proportions of parts to a whole. Unless the
proportions show significant difference, they can be
difficult for audience to interpret.
 Notice in the next slide how the bar chart makes it easier
to see differences in the data. Even if the pie segments
contained percentages, the bar chart makes it easier to
see the subtle differences in some of the data.
15

16. Example:
Because pie charts do not represent subtle
differences well, some experts say to avoid them.
16

17. Use a pie chart.
 When the differences in the data are clear, and can be
proportioned in 7 segments or less.
17

18. Line Graphs
 Most useful in displaying data that changes continuously
over time.
 Example:
18

19. Scatter Plots
 Show how much one variable is affected by another. The
relationship between two variables is called their
correlation.
 Scatter plots usually consist of a large body of data. The
closer the data points come when plotted to making a
straight line, the higher the correlation between the two
variables, or the stronger the relationship.
19

20. Example: Scatter Plot
20

21. Graphical integrity
 A number of factors can lead to misleading visual aids.
Some of these include:
 Scales that do not start at 0
 Some 3-D configurations
 Some pictographs
 False comparisons
 "Doctored" photographs
21

22. The Lie Factor
 Graphic misrepresentation can be measured by this equation:
Lie Factor = size of the effect shown in graphic
size of effect in data
 If the lie factor is equal to one, then the graphic is doing a
good job of accurately representing the numbers.
 If the lie factor is greater than 1.05 or less than .95, it indicates
substantial distortion of the data.
22

23. Example of graphic with a high lie factor.
23

24. Lie factor in prior graphic is high
 The magnitude of change from 1978 to 1985 is shown in the
graph by the relative lengths of the two lines which yields a
high lie factor.
 It also displays strange aspects of perspective. Most roads to
the future are shown as in front of us, this display reverses the
convention.
24

25. Guidelines for Graphics
 Clearly label X and Y axis (start at zero whenever possible)
 Start at zero if possible.
 Use 3-Dimensional graphics only when it improves audience’s
ability to interpret data. If used, be consistent throughout the
document.
 Refer to graphic in text of document. Interpret the significance
of the data.
 Label graphic or visual (Figure 1, Table 2 etc.);
 Write a Caption.
25