Mathematics for all: sense and nonsense of
statistical representations
Heleen Verhage, Freudenthal Institute
PME25 Summer Institute, 18-20 July 2001.
Mathematical literacy (OECD/PISA):
"Mathematics literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded mathematical judgements and to engage in mathematics, in ways that meet the needs of that individual’s current and future life as a constructive, concerned and reflective citizen."
Planetary orbits, 10th or 11th century
William Playfair (1759-1823)
Inventor of:
Line graph
Bar graph
Pie chartExamples of time series and multivariate analysis
Playfair: Trade balance of England,
Playfair: import and export in Scotland, 1786
Playfair: timeseries (250 years: 1565-1821) of price of wheat and wages of
labour
Playfair: area of countries (circles), population (left line seg.) and tax revenu (right line seg.).An example of ‘multivariate analysis’
Tufte:
Graphical excellence begins with telling the truth about the data.
USA population piramids, 1874
Charles Minard (1781-1870)
New techniques:
Use of area as a measure
Use of maps
Minard: carrying traffic by train, area proportional with revenues.
1. Tell the story of this graph2. How many variables in the graph?
Minard: French army on its way to Moscow
Florence Nightingal
e(1820-1910)
Nightingale: original version of the coxcomb graph (1858)
Source: Scientifi
c America
n
Textbook: ‘Getal & Ruimte”
Nightingale: bar graphs to compare conditions in the army with civilian life
Florence Nightingale in later life
“There are three kinds of lies:
lies, damned lies and statistics”
(Benjamin Disraeli (1804-1881))
College enrollment
Tufte: “the worsest graph ever made…”
Tufte:
The number of information-carrying dimensions depicted should not exceed the number of dimensions in the data.
example of lie factor (source: Tufte)
Taken from
textbook
Between saying
and doing…
Selling of
icecream
Manic-Depressive Illness
Timeline of Robert Schumann
Graphical excellence is that which gives to the viewer:
- the greatest number of ideas - in the shortest time - with the least ink - in the smallest space
Relevant literature:
•Darrell Huff (1954). How to lie with statistics. Reprinted in Penguin and Pelican books.
•Edward R. Tufte (1983). The visual Display of Quantitive Information. Cheshire: graphics Press.
•M.J. Moroney: facts from figures. First published in 1951.
•Howard Wainer (1997). Visual revealations. New York: Copernicus-Springer
Relevant websites:
•http://hotspur.psych.yorku.ca/SCS/Gallery/
•http://www-history.mcs.st-and.ac.uk/history/
•http://www.florence-nightingale.co.uk
•http://www.fi.uu.nl/wiskrant/artikelen/hist_grafieken
•http://www.usatoday.com/snapshot/news/snapndex.htm