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