Transcript Document

New Strengths in
the Curriculum’s Statistics
Mike Camden:
Statistics New Zealand
NZ Statistical Association: Education Committee
[email protected]
Auckland Maths Assoc: PD Day: 25 Nov 2008
The views in here are Mike’s.
1
Aims:
1. To get us feeling even better about
the Stats in The NZ Curriculum’s
Maths and Stats: it is:
commonsense, do-able, visual,
fun, novel, useful, vital
2. To help ensure that our students will
contribute to:
health, sustainability, climate, justice …
(from West Aust Mathematics Curriculum Framework)
3. To give bright ideas for next week,next year!
2
Contents:
1. The handout: a range of activities
2. New Strengths in Curriculum’s Statistics:
Two big ideas: one woolly, one sharp
Structures in the Statistics strand
Structures in Cheese
3. An investigation with Paua (Item 1)
the story
activity 1
4. More investigations: multivariate situations:
stories about Items 2 to 7
activities 2 to 12 (some of)
5. Conclusion: analysis => graphs
3
But first: two historical items:
1: from 1908:
William Gosset discovers
the Student t distribution
in the Guinness Brewery, Dublin
2: from 1863: …
4
2: Florence to George: 1863
“Real Gold: Treasures of Auckland City Library”
Letter to Sir George Gray, 28 Jul 1863, ending:
You will do a noble work in New Zealand.
But pray think of your statistics.
I need not say, think of your Schools.
But people often despise statistics
as not leading to immediate good.
Believe me
Yours ever Sincerely
Florence Nightingale
http://0-www.aucklandcity.govt.nz.www.elgar.govt.nz/dbtw-wpd/virt-exhib/realgold/Science/florence-nightingale.html
5
And an ad break …
See NZ Stat Assoc site:
http://nzsa.rsnz.org/
and its new teachers page:
http://nzsa.rsnz.org/teachers.shtml
15,000
See StatsNZ site:
http://www.stats.govt.nz
and its Schools Corner
and its brand new
Infoshare system:
Time Series galore!
Mean and Median Earnings: Auckland and NZ:
Quarterly: 1999 Q2 to 2007 Q2
10,000
Mean Earnings - Ak
Median Earnings - Ak
Mean Earnings - NZ
Median Earnings - NZ
5,000
00
01
02
03
04
05
06
6
07
And a pic of the Waitakere City gender balance:
Females vs Males
for Area Units of Waitakere Cit
2006 Census
3000
Y+X line
2000
1000
Herald
0
0
1000
2000
3000
7
And a pic of the Kapiti gender balance:
F06 (Nr. Females 2006) (up)
vs M06 (Nr. Males 2006) (across)
for the 18 Area Units
of Kapiti Coast District
5000
Paraparumu
Central
4000
the y = x line
Otaki
3000
Waikanae
West
2000
1000
0
0
1000
2000
3000
4000
5000
8
Two big ideas: one woolly, one sharp
The woolly big idea: two sides of maths
The sharp big idea: the highly technical bit
9
The woolly big idea: two sides of maths:
Deterministic mathematics:
Number
Algebra
Measurement
Space
WA: ‘in context …
investigate, generalise,
reason, conclude
about patterns
in number... space ….
They have:
big similarities …
big differences …
Stochastic mathematics:
Chance and Data
(probability and statistics)
WA: ‘locate, interpret,
analyse, conclude from
data …
… with chance’
… and data’
Writers of resources, texts,
activities, assessments
could aim for
this patch: a fresh challenge10
The 2 sides: similarities and differences
Similarities: The Western Australia version:
‘People who are mathematically able
[in both bits] can contribute greatly
towards many difficult issues facing the world
today: health, environmental sustainability,
climate change, social injustice.’
Differences:
They’re different in how they are:
used, learnt, taught, integrated.
They’re different in how they use:
mathematical thinking and rigor.
11
The sharp big idea: the highly technical bit
John Tukey
1915-2000
Stats prof at Princeton
Inventer of
Fast Fourier Transform
Tukey’s test for means…
etc etc etc etc etc etc etc
EDA (1977)
Stem-and-leaf
Box-and-whisker
etc etc
12
The sharp big technical idea from Tukey:
‘If you haven’t done a graph,
then you haven’t done an analysis.’
He intended this for:
Statisticians
at work
Students
Please Vote
Teachers
13
Some determinist mathematical logic:
‘You haven’t done a graph
=>
You haven’t done an analysis’
Or in brief:
No Graph => No Analysis
Can be seen as:
Analysis => Graph(s)
14
An eg from Tukey’s EDA book: Nitrogen:
Rayley (1894) wanted
density of Nitrogen:
Gets N from 15 sources:
7 from air
8 from other sources
He discovered ….
(Hint: starts with A)
15
Structures in the Statistics strand
The Statistics strand is:
A Haphazard Heap
A Subtle Set of Structures
Please Vote
spread
Stem and leaf
mode
16
Most of MAWA votes for Structure …
17
The Waikato teachers vote:
Photo: Harold Henderson
18
Structures in Stat Investigations: in brief:
1: The Statistical Enquiry Cycle:
Problem → Plan → Data → Analysis → Conclusion
2: Datasets: case, series
3: Variables: Categorical, Numerical
4: Exploration, Analysis
5: The group we’re investigating:
6: Graphs: two roles
7: Variation … Variation … Variation … Variation … Variation
19
Structures in Stats Investigs bit: contd:
2: Datasets: case, series
3: Variables:
Categorical, Numerical
A cross-sectional or case dataset
Capsicum prices ($/kg) at several shops:
and one date: 16 Aug 2008
Shop Type
Green Orange
Red
A
Greengrocer
6.50
6.75
7.50
B
Supermarket
7.00
7.50
8.00
C
Supermarket
6.00
6.50
7.00
A time-series dataset
and one shop: Bunbury Peppers
Capsicum prices ($/kg) at several dates:
Date Weather
Green Orange
Red
Jun Fine
6.50
6.75
7.50
Jul Wet
7.00
7.50
8.00
Aug Wet
6.00
6.50
7.00
20
Structures in Stats Investigs bit: contd
4: Exploration, Analysis
1 variable:
Categorical
Numerical
2 variables: x and y:
Categorical / Categorical
Categorical / Numerical
Numerical / Categorical
Numerical / Numerical
3 variables: hmmmmmmmm
4 and more variables ……...
The Pauas: item 1
Graphics make all this accessible.
The others: items 2 to 7
21
Structures in Stats Investigs bit: contd
5: The group we’re investigating:
A population
A sample …
… from a population
In Curriculum from Level 6
22
Structures in Stats Investigs bit: concld
6: Graphs: two roles
Problem → Plan → Data → Analysis → Conclusion
Graphs for Exploration, Analysis, Discovery:
Graphs for Communication of findings:
Underlying everything in life and work (and Stats):
7: Variation … Variation … Variation … Variation … Variation
The Mathematics and Statistics in The NZ Curriculum
progresses through all these structures
23
Structures in the Probability strand: brief:
Question or Experiment → Outcomes → Probabilities
→ Probability distribution → Decisions
Has the coffee arrived yet?
Outcome Probability
Yes
0.3
No
0.7
These things go from being
Out Ofs to Fractions to Proportions to Percentages to Probs;
and that’s hard!
24
Structures in Cheese
My problem:
I like eating cheese
I avoid saturated fat and salt
What do I do?
25
Cheese continued:
Whitestone,
Oamaru,
makes:
cheese
datasets
Map from www.geographx.co.nz
26
Cheese: the data:
Name
Brie
Mt Domet Brie
Camembert
Chef's Brie
Caterer's Brie Log
Farmhouse
Airedale
Livingstone Gold
Totara Tasty
Creamy Havarti
Windsor Blue
Moeraki Blue Bay
Highland Blue
Monte Cristo
Island Stream
Stoney Hill Feta
Mt Dasher Feta
Fuschia Creek Feta
Manuka Feta
Energy
1508
1689
1496
1496
1598
1672
1672
1672
1753
1751
1883
1838
1500
1637
1786
1368
1368
1363
1363
FatTot
30.0
36.5
32.0
32.0
32.0
32.9
32.9
32.9
35.8
38.0
43.5
41.0
30.0
31.1
33.9
26.0
26.0
27.0
27.0
FatSat Sodium Protein
21.0
629
23.4
25.0
629
19.9
22.0
629
18.4
22.0
629
18.4
22.0
629
24.4
23.0
707
26.8
23.0
707
26.8
23.0
707
26.8
23.8
750
24.4
25.2
750
20.3
30.5
1140
16.1
28.7
825
18.9
19.5
1140
23.1
21.2
707
28.6
23.0
707
31.3
17.7
629
23.9
17.7
629
23.9
18.9
629
21.4
18.9
629
21.4
What do
we do
now??
27
Graphs of 2 ‘univariate’ distributions:
Frequency Distribution: Saturated Fat (%):
4
Fetas
3
2
1
0
18
10
9
8
7
6
5
4
3
2
1
0
19
20
21
22
23
24
25
26
27
28
29
30
31
Frequency Distribution: Sodium (g/100g)
630
730
830
930
1030
1130
What do
we do
now?? 28
Graph of a ‘bivariate’ distribution:
Whitestone Cheeses:
Sodium (mg/100g) vs Saturated Fat (%) (both jittered)
Source: Whitestone Brochure 2008
1000
500
Bries
Goldens
Blues
Fetas
0
0
10
20
30
How many
variables?
What sorts?
What do I
eat??
Other
conclusions??
29
An investigation with Paua (Item 1)
The story
The activity
And a
mini-version: …
30
1: Shellfish in Court: a Paua story
Pauas (A) are taken from a bay, legally.
Pauas (B) may have come from
a marine reserve.
What might 2 the distributions look like?
How would your students
graph them?
What would
a judge think?
What actually
happened???
Legal minimum: length > = 125 mm
Some Paua data
Origin PauaSize
A
136
A
132
A
131
A
126
A
130
A
128
A
125
A
130
A
126
A
129
B
138
B
135
B
130
B
136
B
130
B
138
B
130
B
135
B
127
31
B
130
The Paua data:
Here's a mini version of the data, for a short tactile activity.
That's not enough to make sensible decisions, but it's a taste.
You need to chop this card up.
A: underlined, green: 10 values here:
B: Blue, italics: 5 vals:
121
123
124
125
125
125
126
129
129
136
126
130
130
135
138
32
Paua distributions for the judge:
Source: I Westbrooke, NZ Dept of Conservation
Disputed
CabbagePatch
120
125
130
135
Paua size (mm)
CabbagePatch
Disputed
0.30
Relative
frequency
0.25
0.20
0.15
0.10
0.05
0.00
120
125
130
Paua size (mm)
135
140
33
More investigations: multivariate situations:
Stories about Items 2, 3, 5, 6, 7
Activities on these
34
2: Census data from the neighbours:
Data on Westn Aust’s 156 ‘Statistical Local Areas’:
ABS_MAWA_CensusData.xls
SLA Name
Male01
Fem01
Mandurah (C) 20,935
22,302
Murray (S)
4,881
4,773
Bunbury (C) 13,359
13,848
Capel (S) - Pt A 1,299
1,305
Dardanup (S) - Pt
2,864
A
2,961
Harvey (S) - Pt A4,666
4,680
Total01
43,237
9,654
27,207
2,604
5,825
9,346
A local sample of the 156 SLAs
Male06
Fem06 Total06
AvHhSize01
AvHhSize06
24,918
26,719
51,637
2.5
2.4
5,478
5,444
10,922
2.5
2.5
13,681
14,144
27,825
2.5
2.4
2,818
2,893
5,711
3.1
3.2
3,601
3,669
7,270
2.9
2.7
5,439
5,397
10,836
3.0
2.9
A question:
How big is the average WA household??
A look:
Female vs Male numbers for the SLAs:
( It’s easy for kids to do this for their town,
from www.stats.govt.nz )
35
How big is the average WA household??
30
Freq Dist: Household Size 06: WA SLAs
20
10
0
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
3.3
3.5
3.7
3.9
36
Nr.Females vs Nr.Males:
WA SLAs
with y = x line
40,000
20,000
0
0
Bunbury
4,000
20,000
Major cites
Inner regional
Outer regional
Remote
Very remote
40,000
Melville
Difference: Females - Males
vs Nr.Males:
WA SLAs
2,000
Female vs
Male numbers
for the 156
WA SLAs:
with
Regression,
Residuals,
and
Remoteness
0
Bunbury
-2,000
0
20,000
40,000
37
3: Txt Olympics: www.learnngmedia.co.nz
An activity from a new Media/Stats book:
Motutapu College is holding a Texting Olympics to find out
who has the fastest thumb in the school! Events include:
The Sprint
Call me
The Marathon
Can you pick
me up after
school today. I
have football
practice and
won’t be able to
catch the bus.
The Hurdles
Guess what? I
got 90% in my
probability
test!!!
We’ll use this
to do some ‘Statistical Thinking’ …
38
Texting Olympic: Activity 1 (of 5)
‘You need to select five students for the finals of
“The fastest thumb in school”.
They need to be the five students who can best
represent the class in all three events.
Discuss with a classmate your ideas on how to
select these students.
Justify your decision with reference to the data’
A Year 9 class at Newlands College
(Wellington) borrowed stopwatches …
39
The
Txt data:
Name
Rachel
John
Francine
Michelle
Jennifer C.
Abigail
Jessica
Georgina
Nathan
Glenn
Ryan
Emma A.
Jake
Nirvana
Devon
Matthew
Ryan
Ashley
Joanna
Winston
Anthony
Stephanie
Anna
Jennifer D.
Sian
Aditya
Alana
Louis
Emma B.
Owen
Sprint Marathon
0.05.44
0.49.67
0.12.91
3.42.78
0.18.75
2.55.59
0.05.00
1.00.00
0.06.00
1.03.00
0.05.00
1.15.00
0.04.66
1.01.00
0.08.65
1.19.85
0.11.10
1.44.75
0.12.19
1.20.43
0.12.16
1.45.94
0.04.06
0.46.07
0.06.69
1.12.08
0.08.22
0.51.31
0.05.97
1.11.53
0.05.47
1.48.82
0.07.09
1.28.75
0.04.29
1.48.50
0.05.50
1.30.00
0.08.12
0.43.31
0.07.30
1.54.94
0.04.00
0.55.88
0.07.88
1.39.94
0.04.97
1.01.38
0.10.43
1.20.25
0.16.94
3.57.22
0.06.69
0.37.88
0.07.38
1.28.50
0.04.81
1.10.00
0.05.46
1.03.59
Hurdles
0.42.40
1.47.06
1.46.65
0.49.56
0.53.44
0.46.74
0.40.96
0.55.13
1.06.62
1.21.75
1.07.35
0.43.13
0.43.47
0.28.41
1.53.12
1.14.84
1.07.83
1.28.69
0.41.72
0.39.56
0.54.90
0.30.50
1.00.72
0.45.03
1.13.66
2.53.34
0.25.13
0.40.44
0.53.72
0.51.59
Times are in
min.sec.hundredths
What do we
do now??
40
Sprints: the univariate distribution:
Frequency
8
7
6
Frequency of Times for Sprint
Stephanie
Emma
Ashley
Jessica
Emma
Jennifer
Add variables by
re-using data-ink:
Draw graph as blocks;
write names in blocks;
Colour-code:
girls and boys
5
4
3
2
1
0
0
1 2
3 4
5 6
7 8
9 10 11 12 13 14 15 16 17 18 19 20
Time (seconds; rounded)
What now??
41
Hurdles vs Marathon: bivariate distribution
Time:
Hurdles vs Marathon by Gender
Hurdles
w ith linear regressions
(seconds)
200
Girls
Boys
That blue
y = x line
is for the
determinists
and synergists!
150
100
50
Ms Speed
0
0
50
100
150
200
Time: Marathon (seconds)
Conclusion:
words
numbers
graphs
working together
250
(Edwin Tufte)
42
4: Cheese: Done!
Data Graphics for Exploration, Communication:
43
5: Dolphins:
Hector’s Dolphin:
North Island
South Island
populations
Are they
different sub-species?
Dataset contains
head length
head width
etc
for 59 individuals
What do we do??
possums
44
Dataset comes from 59
skeletons in 3 museums.
Selected measurements:
simplified definitions:
RWM - rostrum width at
midlength
RWB – rostrum width at
base
RL – rostrum length
ZW – zygomatic width
CBL - condylobasal length
ML – mandible length
We’ll use Width, Length
45
Are they different sub-species?
Width (mm)
Dolphin Head Measurements:
Width vs Length by Island
70
60
50
Nth
Sth
40
250
260
270
280
290
Length (mm)
300
310
320
46
47
48
49
6: Possum Browse:
Australian brush-tailed possum
Trichosurus vulpecula
Introduced 1837 and 450 times
No natural predators
Damages foliage, fruit, birds
A BACI project:
Before/After
Control/Intervention
Two ‘lines’ chosen
‘Control’ not treated
‘Intervention’:
1080 poison by air
Percentage foliage cover
estimated Before/After
at 38+23 trees.
50
A Possum-browse BACI graphic:
Foliage cover 99 (% ) vs Foliage cover 98 (% )
100
y = 0.8121x + 20.031
2
R = 0.3653
Control
80
Treated
Linear
(Treated)
60
Linear
(Control)
40
y = 0.7378x + 11.95
2
R = 0.6299
20
0
0
20
40
60
80
100
51
7: CO2 at Baring Head (Wgtn)
Data Graphics for Exploration, Communication:
CO2 data (ppm) from
Australia; Cape Grimm
Year Month CO2 Conc
1977
1
330.79
1977
2
330.78
1977
3
331.02
1977
4
330.91
1977
5
330.95
1977
6
331.49
1977
7
331.80
1977
8
332.31
1977
9
332.90
1977
10
332.98
1977
11
332.75
1977
12
332.35
etc
etc
etc
CO2 data (ppm) :
from NZ: Baring Head:
Yr Mth Day Hour
1973
1
6
8
1973
1
9 11
1973
1 12 17
1973
1 13 10
1973
1 16 20
1973
1 17
9
1973
2
5 22
1973
2
8
3
1973
2 11
2
1973
2 12 13
1973
2 12 20
1973
2 13
3
etc etc
CO2
326.37
326.40
326.54
325.47
326.29
325.87
327.67
325.88
326.39
325.96
326.26
325.68
52
Exploration graphs: CO2: Baring Head
380
CO2 at Baring Head (Wellington)
370
360
350
Model fitted by
linear regression:
y = 1.4749x - 2584.7
340
R2 = 0.9956
330
320
1973
1978
1983
What do we see??
1988
1993
1998
2003
What now??
53
More exploration: residuals plot
Residuals: CO2 - Fit (ppm)
5
4
3
2
1
0
1973
-1
1978
1983
1988
1993
1998
2003
-2
-3
This data comes from:
ftp://ftp.niwa.co.nz/tropac/
which is provided by
National Institute of Water and Atmospheric Research
What do we
see now?
54
A static but colourful graphic:
Median
incomes in
NZ Territorial
Authorities;
2006 Census
We’ll demo an
interactive
dynamic
graphic
55
Conclusion: Exhilarating challenges
in Maths and Stats for:
Teachers
Students
Parents, school community, wider community
Researchers and teacher educators
Resource designers
Assessment designers even!
Statistical workers
‘Discovery statistics:
(Chris Wild; Auckland)
the daily experience of statistical practitioners’
56
Links 1: Australia
ABS site: for teachers
www.abs.gov.au/teachers and for students
www.abs.gov.au/students
Census at School:
www.abs.gov.au/websitedbs/cashome.NSF
Fuel use:
http://www.greenhouse.gov.au/cgi-bin/transport/fuelg
Fishing in the bay:
http://blogs.mbs.edu/fishing-in-the-bay/
CO2 data and more, from Aust:
http://www.environment.gov.au/soe/2006/publications
OZCOTS 2008:
http://silmaril.math.sci.qut.edu.au/ozcots2008/
57
Links 2: NZ
Curriculum and some resources:
http://nzcurriculum.tki.org.nz/
http://www.nzmaths.co.nz/
http://www.nzamt.org.nz/
http://www.censusatschool.org.nz/
www.stats.govt.nz
http://www.learningmedia.co.nz/
Computer assisted statistics teaching:
http://cast.massey.ac.nz/
CO2 data, and more, from NIWA:
ftp://ftp.niwa.co.nz/tropac/
58
Links 3: NZ contd:
Hector’s and Maui’s Dolphins
http://www.rsnz.org/publish/jrsnz/2002/036.php
Netball:
http://www.netballnz.co.nz/
Cheese:
https://www.whitestonecheese.co.nz
DVD/CD sets with video and data on about 8 topics; 2 sets,
small fee; from
[email protected]
Florence Nightingale:
http://0-www.aucklandcity.govt.nz.www.elgar.govt.nz/dbtwwpd/virt-exhib/realgold/Science/florence-nightingale.html
See NZSA site: http://nzsa.rsnz.org/
And its new teachers page http://nzsa.rsnz.org/teachers.shtml
59
Links 4: Internat Assoc for Stat Education
http://www.stat.auckland.ac.nz/~iase/
ICME 11, Monterrey, Mexico. July 2008
ICOTS 8, Ljubljana, Slovenia July 2010
Statistics Education Research Journal (SERJ)
International Statistical Literacy Project (ISLP)
ICMI/IASE Study: Statistics Education in School
60
Links 5: Elsewhere:
David Mumford: The Age of Stochasticity:
www.dam.brown.edu/people/mumford
Data and Story Library:
http://lib.stat.cmu.edu/DASL/
EDA: with several free software links:
en.wikipedia.org/wiki/Exploratory_data_analysis
E Tufte:
http://www.edwardtufte.com/tufte/
The GAISE project, USA:
http://www.amstat.org/education/gaise/
61
Links 6: Elsewhere contd:
Gallery of Data Visualization
The Best and Worst of Statistical Graphics
http://www.math.yorku.ca/SCS/Gallery/
R: a language and environment for statistical
computing and graphics.
http://www.r-project.org/
R Commander: a basic-stats GUI for R:
http://cran.rproject.org/web/packages/Rcmdr/index.html
Statistica, with a free e text:
http://www.statsoft.com/
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Links 7: Data Visualisation etc:
Recommended for visualisations:
http://services.alphaworks.ibm.com/manyeyes/
home
http://www.gapminder.org/downloads/applicatio
ns/
http://www.dur.ac.uk/smart.centre/
https://www.geoda.uiuc.edu/
http://www.worldmapper.org/
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Links 8: UK’s Office of National Stats:
Some of the interactive objects on ONS site:
www.statistics.gov.uk/economicactivity/index2.h
tml
http://www.statistics.gov.uk/PIC/index.html
http://www.statistics.gov.uk/populationestimates
/svg_pyramid/default.htm
You need to install the SVG software, which
is available in the last link.
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Links 9: Links of Links from Pip:
For links from conferences
http://aucksecmaths.wikispaces.com/Mexico
For a few others
http://nzstatsedn.wikispaces.com/Useful+websites
/Information for Auckland Secondary Maths Teachers
http://aucksecmaths.wikispaces.com/
http://www.nzqa.govt.nz/ncea/resources/maths/index.
html
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Links 10: OECD eXplorer :
New platform: visualising & analysing stats
OECD has launched a powerful, interactive tool for visualising and analysing regional
statistics. OECD eXplorer combines maps and other graphics via the Internet, to
increase the user’s understanding of regional differences and structures across and
within OECD countries. To try out the regional maps and statistics using OECD
eXplorer, go to:
http://www.oecd.org/document/50/0,3343,en_2649_33735_41564530_1_1_1_1,00.ht
ml .
This development is part of the overall strategy to improve the accessibility and
usability of OECD statistics (see also the visualisation of data contained in the OECD
Factbook using dynamic graphics
http://www.oecd.org/document/1/0,3343,en_2825_293564_40680833_1_1_1_1,00.ht
ml).
The development of OECD eXplorer is the result of a fruitful cooperation between
OECD and the National Centre for Visual Analytics (NCVA, http://ncva.itn.liu.se/) at
Linköping University, Sweden. In the seminar on generating knowledge from
statistics, organised by Statistics Sweden and OECD in Stockholm in May, Professor
Mikael Jern from NCVA presented a first version with some OECD statistics. Since
then, the development team at NCVA has worked intensively on improving the tool
and adapting it to all the needs expressed by OECD.
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Links 11: Hans Rosling
www.ted.com search Rosling
2006 and 2007 talks:
http://www.ted.com/index.php/talks/view/id/92
http://www.ted.com/index.php/talks/view/id/140
Software and data
http://tools.google.com/gapminder/
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