Mathematics for all: sense and nonsense of statistical representations Heleen Verhage, Freudenthal...
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Transcript of Mathematics for all: sense and nonsense of statistical representations Heleen Verhage, Freudenthal...
![Page 1: Mathematics for all: sense and nonsense of statistical representations Heleen Verhage, Freudenthal Institute PME25 Summer Institute, 18-20 July 2001.](https://reader030.fdocuments.net/reader030/viewer/2022032800/56649d3a5503460f94a152f1/html5/thumbnails/1.jpg)
Mathematics for all: sense and nonsense of
statistical representations
Heleen Verhage, Freudenthal Institute
PME25 Summer Institute, 18-20 July 2001.
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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."
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Planetary orbits, 10th or 11th century
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William Playfair (1759-1823)
Inventor of:
Line graph
Bar graph
Pie chartExamples of time series and multivariate analysis
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Playfair: Trade balance of England,
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Playfair: import and export in Scotland, 1786
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Playfair: timeseries (250 years: 1565-1821) of price of wheat and wages of
labour
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Playfair: area of countries (circles), population (left line seg.) and tax revenu (right line seg.).An example of ‘multivariate analysis’
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Tufte:
Graphical excellence begins with telling the truth about the data.
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USA population piramids, 1874
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Charles Minard (1781-1870)
New techniques:
Use of area as a measure
Use of maps
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Minard: carrying traffic by train, area proportional with revenues.
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1. Tell the story of this graph2. How many variables in the graph?
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Minard: French army on its way to Moscow
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Florence Nightingal
e(1820-1910)
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Nightingale: original version of the coxcomb graph (1858)
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Source: Scientifi
c America
n
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Textbook: ‘Getal & Ruimte”
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Nightingale: bar graphs to compare conditions in the army with civilian life
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Florence Nightingale in later life
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“There are three kinds of lies:
lies, damned lies and statistics”
(Benjamin Disraeli (1804-1881))
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College enrollment
Tufte: “the worsest graph ever made…”
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Tufte:
The number of information-carrying dimensions depicted should not exceed the number of dimensions in the data.
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example of lie factor (source: Tufte)
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Taken from
textbook
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Between saying
and doing…
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Selling of
icecream
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Manic-Depressive Illness
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Timeline of Robert Schumann
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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
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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
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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