Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel...

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Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria University

Transcript of Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel...

Page 1: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Using official statistics in the classroom

Sharleen Forbes(assisted by Martin Ralph & Nathaniel Pihama)

Statistics New Zealand

School of Government, Victoria University

Page 2: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

To cover:

• Good points about official statistics• Playing with official statistics

– Examples for classroom use

• Where to in the future?– Providing more sets of real data– New ways of visualising data

Page 3: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Good points about official statistics• Real data available for all levels of the secondary school• Can be used in subjects other than ‘statistics’• Large scale and broad coverage (many variables)• Both census and survey data

– Census of Population and Dwellings– Household Labour Force Survey

• Complex Survey Designs (Clusters and Stratas)• Social and economic data

– Demographics – GDP, CPI, etc.

• Time series data– Infoshare

• Geographical information for census data– QuickStats About a Place– QuickStats About a Subject

Page 4: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Statistics New Zealand initiatives - to support schools

• Resources to support the new curriculum– Schools Corner on Statistics New Zealand website

(http://www.stats.govt.nz/schools-corner)

• CensusAtSchools – Joint funder (http://www.censusatschool.org.nz)

• Dataset provision– Official Statistics available on the website– Synthetic Unit Record Files (SURFs)

Page 5: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Playing with official statistics - Examples

1. Census data- can be used at all levels of secondary school to teach exploratory data analysis (tables and graphs), reclassification and general statistical thinking

2. Official Statistics Survey data- useful for teaching basic sampling techniques, estimation and hypothesis testing

3. Time series data- time series analysis

4. Specially constructed unit record data setsSynthetic Unit Record Files (SURFS) - Exploratory Data Analysis and relationships between

variables

Page 6: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

The statistical investigation (PPDAC) cycle(Creators: Wild and Pfannkuch, Auckland University,1999)

• Problem – statement of the research questions

• Plan – procedures used to carry out the study

• Data – data collection process

• Analysis – summaries and analyses of the data to answer the questions posed

• Conclusion – about what has been learned.

Page 7: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

1. Census data example

• Problem (Question)Is Auckland ‘greener’ than Wellington?

• Plan / DataUse 2006 Census data on ‘the way people travel to work’ to indicate how ‘green’ a city is. (www.stats.govt.nz/census/)

Page 8: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Analysis

Page 9: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Definitions & (Re)classifications

• How many and what classes of ‘green’ shall we have?- Have defined ‘green-ness’ by mode of travel to work

- Let’s have only 3 classes of ‘green-ness’ Not green = Driving private or company vehicles Green = Passenger in private vehicle or using public transport Very green =Walking, biking or working at home Omit other categories

Page 10: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• More analysis

Page 11: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Conclusion (and classroom questions)• Conclusion

– Wellington is ‘greener’ than Auckland

• Questions– Is ‘mode of travel to work’ a good indicator of

‘green-ness’?– What other variables might affect ‘mode of travel’?– Should we use more than one indicator?

Page 12: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Population: Census 2006 vs Population: Census 2001

for Area Units of Waitakere City

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2000

4000

6000

8000

0 2000 4000 6000 8000

Sturges NorthFi

Plot of 2006 Census and 2001 Census populations in Waitakere CityWhat is happening in Sturges North?

2. Another fun Census data exampleQuickStats About a Place (www.stats.govt.nz)

Page 13: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

HOTPs (Hot Off The Presses):

Inadvertently useful for schools!A rich source of real information.

They usually contain these tabs:Highlights  |  Commentary  |  Technical notes  |  Tables  

Statistical literacy: ‘Evaluate stat reports’ (L 6,7,8)

Statistical Enquiry Cycle: PPDAC … PPDAC … PPDAC … PPDAC … PPDAC …

Statistical investigation: Story, Data Time series

Statistical investigation: Methodology: defining of questions, sampling methods, errors (samp and non) etc etc etc etc

Probability: One-way tables Two-way tables

Page 14: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

2. Official Statistics Survey data

• Problem (questions)a) Are more people unemployed now than in

previous years?b) Are you less likely to be unemployed if you

are from a particular ethnic group ?

• Plan / DataAnalyse time series of national employment rates by (sole) ethnic group– Statistics New Zealand’s Household Labour Force Survey

(www.stats.govt.nz)

Page 15: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

NZ unemployment rate (%), quarterly; with its smooth (4x2 term moving average)

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5

10

Mar86

Jun87

Sep88

Dec89

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Jun92

Sep93

Dec94

Mar96

Jun97

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Dec99

Mar01

Jun02

Sep03

Dec04

Mar06

Jun07

Percent

• Analysis a).

Page 16: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Analysis b). Time series data – from tables available on Statistics New Zealand website for December 08 Quarter

Unemployment rates for 'sole' ethnic groups -HLFS Dec 08 quarter

Quarter European Maori Pacific Asian

Dec-07 2.2 8.3 5.2 5.5

Mar-08 3.0 9.8 8.8 5.9

Jun-08 2.8 8.0 6.8 5.2

Sep-08 3.2 9.3 7.6 4.7

Dec-08 3.2 9.6 7.8 6.3

Page 17: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Times series plots

Times series of national NZ unemployment for 'sole ethnic groups

0.0

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Dec-07 Mar-08 Jun-08 Sep-08 Dec-08

Quarter

Percentage

NZ European

Maori

Pacific

Asian

Page 18: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Conclusions (and classroom questions)• Conclusions

– Unemployment risen for all these ethnic groups over the last five quarters and the greatest increase in unemployment has been for Pacific peoples

– There is a difference between the ‘sole’ ethnic groups: the unemployment rate for NZ European is the lowest and the most stable of these four groups over this period and that for Maori is consistently the highest.

• Questions– Why do we use rates rather than numbers for

unemployment?– Will ‘sole’ ethnic rates reflect ‘mixed’ ethnic rates?

Page 19: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Another sample survey example - a simple look at seasonality

• Problem (question)Is there an annual pattern in retail sales?

• Plan / dataCheck for seasonality in quarterly summary time series data for monthly retail trade sales (in dollars)

– INFOShare (www.stats.govt.nz)

Page 20: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Analysis Time series plot

Quarterly Retail Trade Sales

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Dec Jun Dec Jun Dec Jun Dec Jun Dec Jun Dec Jun Dec Jun

Quarter

Value ($Million)

Actual Seasonally adjusted Trend

Page 21: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Conclusions (and classroom questions)

• Conclusions– Annual seasonality - peak every December /

January– Rising trend over time - plateau in last 3 quarters

• Questions– What components of retail trade would contribute

most to the December peaks?– What does it mean when the seasonally adjusted

and trend lines lie virtually on top of each other?– Easter fell in the March rather than June quarter in

2008. Is there any evidence that this affected the pattern of retail sales?

Page 22: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

3. Specially constructed data sets - SURFS

HLFS/NZIS CURF June 2004

• 123 variables

• Approx. 29,000

confidentialised individuals

HLFS/IS04 SURF • 8 variables

• 200 synthetic individuals

New Zealand Income Survey June 2004

• 76 variables used

• 15,000 private households

• Approx. 29,000 individuals

Household Labour Force Survey June 2004

• 51 variables used

• 15,000 private households

• Approx. 29,000 individuals

Relationship between the original data set, the CURF and the SURF

2001 Household Savings Survey2004 Income Survey2006 Census

Page 23: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Don’t preserve all relationships

Variable Personal IncomeWork and labour force statusSex Qualification – highestMain means of travel to workHours worked in employment per week EthnicityCigarette smoking behaviourAge Access to internetAccess to a Cellphone/Mobile PhoneAccess to a Cellphone/Mobile Phone x x xAccess to internet x x xAge x x x x x x xCigarette smoking behaviour x xEthnicity x x x x xHours worked in employment per week xMain means of travel to work xQualification – highest x x xSex x xWork and labour force status

Bivariate relationships preserved (x) in the 2006 Census SURF

Page 24: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

SURFING: Classroom Example

• Using 2004 Income Survey SURF data. • Data downloaded from Schools Corner on the Statistics

New Zealand website (www.stats.govt.nz/schoolscorner/).

• Dataset has 200 records and seven variables: – gender (male, female)– highest education qualification (none, school, vocational,

degree) – marital status (married, never, previously, other)– ethnic group (European, Maori, Other)– age (15-45)– hours worked weekly (0-79)– weekly income ($0-$2000).

Page 25: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Example• We can construct some background

– In this example we let the SURF dataset represent a company’s employees.

– Every employee creates the same administration costs regardless of how many hours are worked.

– The company is concerned that its staff administration costs are too high.

• Problem (questions) – Do most employees work a ‘normal’ (40 hour) week?– What variables are related to the number of hours

worked?

Page 26: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Specific questions for secondary school classrooms

1. What proportion of employees work at least 40 hours per week? (Summary)

2. Are these proportions different for males and females? (Comparison)

3. Do males tend to work more hours per week than females? (Comparison)

4. What is the relationship between hours worked and income? (Relationship between two measurement variables)

Page 27: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Plan / Data (a). Take a random SAMPLE of 35 records from SURF- are samples by sex large enough (say 17 and 18?)

• Plan / Data (b). - Resample -compare (or combine) summary statistics

•Plan / Data (c). - Use all SURF data

Page 28: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Could construct 95% confidence intervals by sex.• Would graphs be easier to interpret than the table?

Summary Statistics (Total SURF): Hours worked

Total SURF

By gender

(Records) (200) Male(93) Female(107)

Mean 33.7 42.1 26.4

Standard deviation 16.2 13.2 14.9

Minimum 2 5 2

Lower quartile 20 39 14

Median 40 40 25

Upper Quartile 45 50 40

Maximum 70 70 60

• Analysis

Page 29: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

0

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male

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Collection 1Histogram

Hours_Worked

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Collection 1Dot Plot

Hours_Worked

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Collection 1Box Plot

• Analysis Graphs of SURF data

Page 30: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Conclusions (and classroom questions)• Conclusions

1. Use tables for reference, graphs to tell a story.2. Proportions of males and females working 40 hours or

more are different. About half of the males do but only about a quarter of the females do.

• Questions– What is the ‘clumping’ at 40 hours?– Given the size of the SURF do you think the above

patterns will be similar if other SURFs were created?

Page 31: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Analysis - Question 4.

Relationship between income and hours worked?

Weekly_Income = 17.1Hours_Worked + 0.35 ; r2

= 0.63

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Hours_Worked

0 10 20 30 40 50 60 70 80

Collection 1Scatter Plot

Page 32: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Conclusion (and classroom questions)

• Conclusion– Income increases as work more hours.

• Questions– What is the estimated income for someone who

doesn’t work? – What extra income (on average) is expected if

work an extra hour per week?

– Is the (regression) line a good fit to the data?

Page 33: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Extension:Are other factors related to income?

(Hours worked and Age)

Page 34: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Extension:Are other factors related to income?(Hours worked and Qualification Level)

Page 35: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

ExtensionAre other factors related to income?(Hours worked and Qualification Level)Example from a first-year university course

Creator: John Harraway, Otago University

• Plan / Data– Recategorise highest qualification

• Secondary = None OR Secondary (105) =S

• Tertiary = Vocational OR Tertiary (95) =T

– Do a multiple regression (main effects model - no interaction terms) in SPSS or similar

Page 36: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

SPSS regression output (values extracted & rounded for all 3 models)

Model

UnstandardisedCoefficients

95% Confidence

Interval tSignce

p-valueR2ß Std error

1. (Constant) .3 34 (-68,68) 0.01 .992 .63

Hours 17 1 (15,19) 18.5 .000

2. (Constant) 414 30 (356, 472) 14.0 .000 .24

Tertiary 344 44 (257, 431) 7.8 .000

3. (Constant) -19 32 (-83, 45) -0.59 .553 .69

Hours 15 1 (14,16) 16.4 .000

& Tertiary 183 30 (125, 242) 6.1 .000

Page 37: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• ConclusionsWeekly Income = $ (-19 + 15xHoursWorked + 183xTertiary)

– Line is a reasonable fit (R2=69%-amount of variation in points explained by the line).

– Both hours worked and highest qualification are related (p-values less than 0.05) to weekly income earned

– Average income if work NO hours not significantly different to zero (high p-value)

– Mean increase in income per hour worked is reduced (from $17 to $15) if tertiary also considered

– Mean increase in income if have a tertiary qualification is also reduced (from $344 to $183) when adjusted for number of hours worked

– 95% confidence interval for the intercept (income when no hours are worked) still contains zero

Page 38: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

• Classroom questions

• Questions

– Is there any ‘interaction’ between hours worked and qualification?

– Are there any outliers?

– What does a scatterplot of the residuals (distances from the line) indicate?

Page 39: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

More resampling

Use SURF as sample from CURF population

• Bootstrapping – Take repeated samples with replacement (of same size as

original, n=200).

• Jack-knifing– Take repeated samples dropping one value from original

sample each time (n=199).

• Calculate mean and standard deviation of sample means

• Compare summary statistics with CURF (or full 2004 Income Survey).

Page 40: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Where to in the future?• Dynamic graphs and maps

(Data Visualisation)(Creator: Martin Ralphs, Statistics NZ)

Why visualise data?To compare data

meaningful graphs can be summarised in few wordsTo give a fast overview

can save the reader some of the interpretation workTo reduce information

can make huge data sets understandableTo convey a memorable story

dare to interpret the data visuallyTo reveal insight

that would otherwise remain hidden

Page 41: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.
Page 42: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

But if the presentation is right…

Film YearGross ($m)*

Dances With Wolves 1990 184

Robin Hood 1991 166

JFK 1991 70

The Bodyguard 1992 122

A Perfect World 1993 31

Wyatt Earp 1994 25

The War 1994 17

Waterworld (!) 1995 -87

* US takings - source IMDB

http://www.statistik.zh.ch/vornamen/vorname.php?nam=&M=&F=&year=2006

Page 43: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

TA_ID NumCt C80 C81 C82 C83 C84 C85 C86 C87 C88 C89 C90 C91 C92 C93 C94 C95 C96 C97 C98 C99 C00 C01 C02 C03 C04 C05 C06 T80 T81 T82 T83 T84 T85 T86 T87 T88 T89 T90 T91 T92 T93 T94 T95 T96 T97 T98 T99 T00 T01 T02 T03 T04 T05 T06 PC80 PC81 PC82 PC83 PC84 PC85 PC86 PC87 PC88 PC89 PC90 PC91 PC92 PC93 PC94 PC95

001 2 30 33 37 52 52 25 40 36 25 27 38 46 47 71 83 59 51 89 121 136 153 136 107 133 190 219 239 1429 1370 1053 916 1041 1077 1154 1124 1519 1516 963 1114 1103 1307 1396 1369 1367 1398 1651 1662 1694 1693 1548 1778 2236 2237 2018 2.09937 2.408759 3.51377 5.676856 4.995197 2.321263 3.466205 3.202847 1.64582 1.781003 3.946002 4.129264 4.261106 5.432288 5.945559 4.309715

002 1 80 83 69 43 35 51 86 51 59 69 51 106 118 162 165 219 208 246 323 237 271 241 235 220 345 262 359 3208 3888 1772 1672 1905 2746 2347 2296 2954 2965 1993 2482 1883 2133 2334 2979 2562 2468 2441 2505 2705 2929 2702 2905 2637 2543 3043 2.493766 2.134774 3.893905 2.57177 1.83727 1.857247 3.664252 2.221254 1.997292 2.32715 2.558956 4.270749 6.266596 7.594937 7.069409 7.35146

003 1 4 7 12 8 13 4 10 5 11 9 9 12 7 24 12 12 15 18 30 12 9 25 7 21 22 20 29 496 496 289 246 341 392 311 321 336 363 340 469 352 365 345 381 372 436 353 400 331 383 348 348 339 327 341 0.806452 1.41129 4.152249 3.252033 3.812317 1.020408 3.215434 1.557632 3.27381 2.479339 2.647059 2.558635 1.988636 6.575342 3.478261 3.149606

004 1 2 1 1 2 5 11 9 2 1 4 5 7 10 11 0 3 7 6 6 9 6 6 6 3 2 6 10 386 286 213 193 234 212 227 245 275 271 274 244 290 278 244 274 272 223 263 223 288 345 306 354 362 334 424 0.518135 0.34965 0.469484 1.036269 2.136752 5.188679 3.964758 0.816327 0.363636 1.476015 1.824818 2.868852 3.448276 3.956835 0 1.094891

005 1 120 116 123 118 129 123 110 76 63 114 127 127 98 71 69 82 116 152 204 166 171 162 182 156 198 203 268 6228 5334 3598 2786 3193 3246 3372 3192 4433 4904 3455 3513 3118 3239 3310 3325 3457 3602 4295 4311 4475 3976 3933 3553 3716 3876 3965 1.926782 2.174728 3.418566 4.235463 4.040088 3.789279 3.262159 2.380952 1.421159 2.324633 3.675832 3.615144 3.14304 2.192035 2.084592 2.466165

006 1 83 83 104 154 133 114 123 110 97 93 75 88 108 138 135 137 127 143 156 168 213 217 217 190 234 259 231 5164 4254 3010 2980 2961 3080 4111 3804 4904 5364 3672 3623 3513 4012 4028 4071 3618 3100 3464 3423 3671 4283 4140 4155 4946 4925 4942 1.607281 1.951105 3.45515 5.167785 4.491726 3.701299 2.991973 2.891693 1.977977 1.733781 2.042484 2.428926 3.074295 3.439681 3.351539 3.365267

007 2 1384 1263 1220 1308 1431 1116 1087 1102 1135 1292 1226 1271 1192 1440 1219 1180 1244 1391 1103 1164 1241 1305 1358 1461 1728 1738 1812 28751 24292 19800 18725 20267 18863 18093 21449 24663 30508 18484 19121 17435 18172 19520 19424 19609 17660 17013 17079 16747 17575 16697 16719 19836 19746 19882 4.813746 5.199243 6.161616 6.985314 7.060739 5.916344 6.007848 5.137769 4.602035 4.234955 6.632763 6.647142 6.836822 7.924279 6.244877 6.074959

009 1 91 55 79 142 185 119 153 126 123 158 150 162 170 179 213 225 206 193 184 225 231 124 80 85 108 125 128 4237 2987 2154 2074 2195 2572 2389 2339 2592 3447 2355 2777 2709 2755 3244 3441 3025 2845 3059 3588 3256 1473 1137 1232 1571 1561 1814 2.147746 1.841312 3.667595 6.846673 8.428246 4.62675 6.404353 5.386917 4.74537 4.583696 6.369427 5.833633 6.275378 6.497278 6.565968 6.538797

010 1 40 46 52 55 67 85 102 62 60 62 34 55 56 44 56 58 89 77 65 64 50 46 59 61 67 74 89 1069 1198 911 973 1019 1131 1213 1154 1126 1179 913 982 1057 909 868 851 974 769 875 922 867 1004 800 800 978 1106 1287 3.741815 3.839733 5.708013 5.652621 6.575074 7.515473 8.408904 5.372617 5.328597 5.258694 3.723987 5.600815 5.298013 4.840484 6.451613 6.815511

011 1 15 15 13 17 14 19 19 11 18 51 37 23 37 31 21 33 40 25 45 59 26 27 28 24 31 30 27 438 917 421 474 582 493 511 449 646 838 679 657 670 621 543 588 515 632 617 580 464 541 596 673 608 687 719 3.424658 1.635769 3.087886 3.586498 2.405498 3.853955 3.7182 2.449889 2.786378 6.085919 5.44919 3.500761 5.522388 4.991948 3.867403 5.612245

012 1 5 11 22 27 23 10 23 28 34 42 30 33 29 31 32 34 35 32 34 36 21 19 14 21 25 37 29 463 742 512 413 639 411 626 543 691 669 684 736 703 779 861 749 902 679 709 782 689 659 881 1001 744 746 1169 1.079914 1.48248 4.296875 6.53753 3.599374 2.43309 3.674121 5.156538 4.920405 6.278027 4.385965 4.483696 4.125178 3.979461 3.716609 4.539386

013 1 8 28 38 38 41 25 19 23 47 51 48 44 55 70 36 45 72 36 36 25 30 19 29 33 33 41 35 940 1482 1262 949 715 687 803 801 930 1057 920 911 1017 1047 925 838 941 638 655 565 539 478 473 516 622 571 532 0.851064 1.889339 3.011094 4.004215 5.734266 3.63901 2.366127 2.871411 5.053763 4.824976 5.217391 4.829857 5.408063 6.685769 3.891892 5.369928

015 1 9 11 7 9 8 7 19 7 14 25 17 15 21 18 8 13 22 19 35 28 26 8 14 15 22 32 31 400 466 369 253 275 300 360 313 382 374 413 325 423 459 476 447 375 371 465 480 429 517 447 566 667 642 612 2.25 2.360515 1.897019 3.557312 2.909091 2.333333 5.277778 2.236422 3.664921 6.684492 4.116223 4.615385 4.964539 3.921569 1.680672 2.908277

016 1 272 348 398 486 461 372 462 534 607 714 602 535 648 727 511 584 703 589 668 769 691 639 526 576 717 731 753 5778 7638 4175 4252 4110 3668 4123 5358 5500 5424 4799 4744 4800 5195 4898 5393 5385 4687 4790 4668 4478 4523 4468 4603 5503 5077 5401 4.707511 4.556167 9.532934 11.42992 11.21655 10.14177 11.20543 9.966405 11.03636 13.16372 12.54428 11.2774 13.5 13.99423 10.43283 10.82885

017 1 37 40 59 39 61 48 46 40 44 69 72 66 74 64 53 45 60 48 27 35 25 23 14 27 25 22 20 812 1098 885 722 587 449 374 465 528 782 723 836 701 627 559 647 567 439 415 380 403 385 347 311 324 367 352 4.55665 3.642987 6.666667 5.401662 10.39182 10.69042 12.29947 8.602151 8.333333 8.823529 9.958506 7.894737 10.55635 10.20734 9.481216 6.955178

019 1 55 26 81 75 74 53 97 88 85 86 118 120 100 84 81 59 54 72 79 77 36 42 34 46 60 62 56 1549 2429 1533 1812 1139 1143 1195 1199 1490 1626 1359 1326 1115 1137 1116 1105 1067 961 1014 967 852 978 879 897 908 950 980 3.550678 1.070399 5.283757 4.139073 6.496927 4.63692 8.117155 7.33945 5.704698 5.289053 8.682855 9.049774 8.96861 7.387863 7.258065 5.339367

020 1 12 31 13 37 27 30 25 24 30 38 29 40 25 38 28 26 29 37 35 30 25 16 14 11 27 23 18 501 798 369 470 481 384 333 434 496 382 341 461 448 505 404 394 389 326 354 326 341 342 315 283 298 303 355 2.39521 3.884712 3.523035 7.87234 5.613306 7.8125 7.507508 5.529954 6.048387 9.947644 8.504399 8.67679 5.580357 7.524752 6.930693 6.598985

021 1 47 57 60 98 83 62 62 79 101 107 123 107 113 104 84 81 60 64 100 80 60 60 44 82 76 103 92 1562 2195 1453 1082 990 803 976 1070 1209 976 983 890 942 1125 1183 1149 1070 1008 1056 948 966 864 1017 1160 1311 1415 1333 3.008963 2.596811 4.129387 9.057301 8.383838 7.721046 6.352459 7.383178 8.354012 10.96311 12.51272 12.02247 11.99575 9.244444 7.100592 7.049608

023 1 95 103 124 131 140 121 98 90 100 142 194 175 170 161 170 182 208 228 252 245 284 308 258 408 432 492 558 2681 3809 3382 2641 2383 2417 2683 2939 3309 3474 3324 3233 3280 3453 3193 3054 3143 2978 3424 3479 3167 3475 4174 4459 4408 4485 4957 3.543454 2.704122 3.66647 4.960242 5.874948 5.006206 3.652628 3.062266 3.022061 4.087507 5.836342 5.412929 5.182927 4.662612 5.324147 5.959398

024 1 119 122 123 152 150 155 181 233 268 259 357 351 374 396 361 242 297 275 211 251 227 308 325 342 379 428 374 3201 4433 3627 2718 2916 2971 2958 2954 3719 3965 3661 3802 3365 3463 3413 3412 3738 3281 3096 3044 2429 2624 2402 2512 3309 3168 3218 3.717588 2.752087 3.391232 5.592347 5.144033 5.217099 6.118999 7.88761 7.206238 6.532156 9.751434 9.231983 11.11441 11.43517 10.5772 7.092614

025 1 42 55 34 98 78 75 70 62 93 85 91 86 119 76 92 89 99 131 106 119 102 94 112 144 168 156 158 1207 1568 1079 1376 1166 1218 1476 1510 1955 1794 1609 1554 1529 1616 1785 1627 1416 1213 1506 1505 1353 1211 1247 1430 1471 1316 1498 3.479702 3.507653 3.151066 7.122093 6.689537 6.157635 4.742547 4.10596 4.757033 4.738016 5.655687 5.534106 7.782865 4.70297 5.154062 5.470191

027 1 12 4 0 2 20 11 23 19 21 24 25 25 14 15 24 26 31 23 37 41 30 21 33 24 45 50 36 164 172 196 168 226 377 443 403 486 516 537 431 347 407 385 324 346 339 419 330 337 326 271 312 383 358 363 7.317073 2.325581 0 1.190476 8.849558 2.917772 5.191874 4.71464 4.320988 4.651163 4.655493 5.800464 4.034582 3.685504 6.233766 8.024691

028 2 198 133 158 155 122 130 148 116 98 81 130 142 175 161 67 98 148 135 173 130 138 144 183 211 230 230 237 4421 3484 2273 2038 1897 2148 2005 1638 2393 2426 2106 2178 2014 2057 2086 1829 1938 1603 1821 1394 1691 1749 2062 2283 2534 2115 2465 4.478625 3.817451 6.951166 7.605496 6.431207 6.052142 7.381546 7.081807 4.095278 3.338829 6.17284 6.519743 8.689176 7.826932 3.211889 5.358119

029 1 22 31 24 32 65 27 21 10 11 9 14 23 20 21 11 20 23 14 16 21 8 11 10 16 22 18 22 653 506 471 420 568 460 416 287 314 340 336 380 453 509 409 343 261 275 299 281 277 262 267 277 301 317 355 3.369066 6.126482 5.095541 7.619048 11.44366 5.869565 5.048077 3.484321 3.503185 2.647059 4.166667 6.052632 4.415011 4.125737 2.689487 5.830904

030 1 123 142 164 173 162 138 197 199 136 119 147 214 208 242 244 223 192 236 231 235 185 221 301 301 403 327 298 3946 3404 1930 1895 1930 1922 1986 1799 2246 2775 2150 2336 2433 2476 2375 2161 2468 2542 2379 2257 2468 2454 2346 2336 2433 2322 2483 3.117081 4.171563 8.497409 9.129288 8.393782 7.180021 9.919436 11.0617 6.055209 4.288288 6.837209 9.160959 8.549116 9.773829 10.27368 10.3193

031 1 129 191 180 177 253 186 204 240 195 195 193 237 235 213 185 173 210 260 301 264 222 242 294 365 388 371 381 1644 1710 1671 1519 1445 1420 2163 2210 2626 2274 1815 1945 2105 2106 2001 2241 2316 2104 2149 2185 2157 2163 2418 2803 2610 2576 2666 7.846715 11.16959 10.77199 11.6524 17.50865 13.09859 9.431345 10.85973 7.425743 8.575198 10.63361 12.18509 11.1639 10.11396 9.245377 7.719768

032 1 7 10 15 11 17 10 11 22 14 15 8 5 6 9 11 5 8 8 4 2 9 9 19 22 25 14 13 652 369 231 245 239 184 237 219 242 176 132 131 175 216 171 176 241 209 206 228 271 241 248 260 227 226 282 1.07362 2.710027 6.493506 4.489796 7.112971 5.434783 4.64135 10.04566 5.785124 8.522727 6.060606 3.816794 3.428571 4.166667 6.432749 2.840909

033 1 91 123 130 140 153 199 167 205 187 142 162 172 216 194 234 234 218 257 314 321 310 285 266 223 316 349 262 6758 4637 2675 2097 1846 1899 2057 2245 2281 2198 1895 1880 1879 1662 1729 1994 2096 2034 2411 2567 2231 2125 2120 2574 2412 2439 2684 1.346552 2.652577 4.859813 6.676204 8.288191 10.4792 8.118619 9.131403 8.198159 6.460419 8.548813 9.148936 11.49548 11.67268 13.53383 11.73521

035 1 55 39 52 43 47 48 36 42 60 40 43 53 63 59 70 54 61 61 70 101 87 83 51 56 99 99 66 1998 1539 1032 856 773 837 776 850 886 867 808 787 641 770 824 881 952 676 908 815 756 762 835 1046 1046 984 977 2.752753 2.534113 5.03876 5.023364 6.080207 5.734767 4.639175 4.941176 6.772009 4.61361 5.321782 6.734435 9.828393 7.662338 8.495146 6.129398

036 1 23 32 29 71 29 21 48 30 24 28 24 32 33 19 32 27 30 30 36 34 35 25 11 32 24 27 33 620 692 589 481 440 554 594 402 392 579 347 355 376 257 376 292 304 279 298 336 277 269 231 349 327 332 343 3.709677 4.624277 4.923599 14.76091 6.590909 3.790614 8.080808 7.462687 6.122449 4.835924 6.916427 9.014085 8.776596 7.392996 8.510638 9.246575

037 1 97 112 84 126 115 114 130 171 171 176 164 174 150 168 145 147 176 153 208 228 182 148 170 212 246 263 293 4233 3331 1918 1566 1620 1654 1755 1751 1780 1725 1447 1535 1427 1576 1731 1596 1547 1381 1490 1498 1352 1360 1306 1501 1640 1581 1744 2.291519 3.362354 4.379562 8.045977 7.098765 6.892382 7.407407 9.765848 9.606742 10.2029 11.33379 11.3355 10.51156 10.6599 8.376661 9.210526

038 2 20 21 16 25 22 17 27 26 34 29 29 31 29 19 19 18 26 21 33 15 24 21 28 22 37 47 40 520 1368 923 687 665 672 831 736 665 572 422 458 502 361 401 428 453 431 555 494 483 446 469 544 533 579 604 3.846154 1.535088 1.733478 3.63901 3.308271 2.529762 3.249097 3.532609 5.112782 5.06993 6.872038 6.768559 5.776892 5.263158 4.738155 4.205607

039 1 3 6 2 11 5 12 15 11 20 10 12 11 10 18 28 34 22 20 24 13 13 12 17 11 26 28 40 221 908 555 462 538 456 410 499 520 535 350 243 230 252 323 356 275 303 400 306 303 341 315 401 434 419 473 1.357466 0.660793 0.36036 2.380952 0.929368 2.631579 3.658537 2.204409 3.846154 1.869159 3.428571 4.526749 4.347826 7.142857 8.668731 9.550562

040 1 130 108 126 142 147 178 193 248 241 248 251 236 263 242 281 267 247 285 279 262 245 271 283 264 322 361 350 1873 4691 2915 2381 2752 2764 3023 3647 3419 2836 2055 2028 2259 2219 2249 2163 1921 1838 2000 2050 2081 2072 2199 2027 2457 2441 2793 6.940737 2.302281 4.32247 5.963881 5.34157 6.439942 6.384386 6.80011 7.048845 8.744711 12.21411 11.63708 11.64232 10.90581 12.49444 12.34397

041 1 14 18 13 5 12 14 10 12 6 13 12 25 19 20 25 21 13 21 12 7 18 26 25 20 24 23 20 552 527 327 307 349 254 382 330 365 287 224 330 304 390 319 363 363 319 290 302 294 318 303 256 337 309 249 2.536232 3.41556 3.975535 1.628664 3.438395 5.511811 2.617801 3.636364 1.643836 4.529617 5.357143 7.575758 6.25 5.128205 7.836991 5.785124

042 1 30 42 67 73 71 90 66 59 57 66 76 104 91 87 100 74 103 105 77 78 66 64 49 63 60 81 84 1020 2739 1543 1297 1409 1445 1465 1330 1107 1247 791 949 890 858 907 876 867 904 886 839 716 768 765 743 831 967 1036 2.941176 1.533406 4.342191 5.628373 5.039035 6.228374 4.505119 4.43609 5.149051 5.292702 9.608091 10.9589 10.22472 10.13986 11.02536 8.447489

044 1 0 0 1 0 0 0 0 39 148 152 127 148 104 95 82 113 104 129 98 98 108 90 84 76 75 88 95 0 0 1 0 0 0 0 460 2908 3533 2949 2763 2596 2601 2685 2770 2836 2273 2144 2210 2287 2178 1870 1840 2090 2063 2164 #DIV/0! #DIV/0! 100 #DIV/0! #DIV/0! #DIV/0! #DIV/0! 8.478261 5.089409 4.302293 4.306545 5.356497 4.006163 3.652441 3.054004 4.079422

045 1 27 38 42 45 64 69 59 54 62 76 61 64 69 65 51 62 56 54 58 52 53 59 66 50 61 56 35 828 1502 1942 2050 1851 1567 1374 1356 1159 1228 967 962 929 1051 940 1015 1029 890 946 964 936 924 982 862 959 1128 958 3.26087 2.52996 2.162719 2.195122 3.45759 4.403318 4.294032 3.982301 5.349439 6.188925 6.30817 6.652807 7.427341 6.184586 5.425532 6.108374

046 1 81 102 91 119 197 180 171 177 158 139 126 137 132 208 200 156 191 141 122 150 111 120 128 107 107 121 83 2198 4937 3738 2500 2728 2854 3203 2897 3348 3684 3048 3145 2952 2621 2513 2277 2609 2107 2037 2184 2035 2120 2144 2100 2409 2520 2369 3.685168 2.066032 2.434457 4.76 7.221408 6.306938 5.338745 6.109769 4.719235 3.773073 4.133858 4.356121 4.471545 7.935902 7.958615 6.85112

047 1 319 366 456 554 497 443 468 422 305 325 332 321 351 306 346 356 357 347 350 318 353 369 395 368 439 407 389 5480 16382 11890 10908 8132 8026 7991 7423 6274 5568 4398 4436 4312 4100 4114 4202 4198 3981 3755 3321 3602 3489 3356 3151 3613 3240 3444 5.821168 2.234159 3.835156 5.078841 6.111658 5.519561 5.856589 5.685033 4.861332 5.836925 7.548886 7.236249 8.140074 7.463415 8.410306 8.472156

048 1 40 42 51 81 100 65 73 67 45 70 85 77 82 84 77 49 71 61 67 59 51 43 31 53 61 52 49 922 1696 1231 1252 1259 1257 1134 1483 1596 1725 1368 1272 1317 1325 1191 1181 1194 1098 1339 1200 1040 987 958 1043 1327 1533 1356 4.338395 2.476415 4.142973 6.469649 7.942812 5.171042 6.43739 4.517869 2.819549 4.057971 6.21345 6.053459 6.226272 6.339623 6.465155 4.149026

052 1 47 62 54 59 51 69 48 69 64 116 113 123 149 114 120 94 105 120 89 148 138 137 113 113 182 210 207 2856 2994 1656 1649 1662 1610 1680 1832 2028 2216 1823 2063 2044 2081 2056 2002 2107 1934 2045 2328 2160 2159 2064 2062 2424 2549 2358 1.645658 2.070808 3.26087 3.577926 3.068592 4.285714 2.857143 3.766376 3.155819 5.234657 6.198574 5.962191 7.289628 5.478136 5.836576 4.695305

053 1 25 27 29 39 27 41 35 34 33 54 39 29 32 38 44 48 49 59 51 41 86 65 62 56 76 76 81 1695 1444 971 899 845 783 835 778 973 774 665 686 644 748 879 910 914 936 891 967 1090 1050 1084 1091 1205 1303 1126 1.474926 1.869806 2.986612 4.338154 3.195266 5.236271 4.191617 4.37018 3.391572 6.976744 5.864662 4.227405 4.968944 5.080214 5.005688 5.274725

054 1 0 0 0 2 0 0 2 0 0 2 0 1 3 3 0 1 1 1 0 2 1 0 3 3 2 0 2 142 120 49 62 92 82 63 62 60 64 53 41 47 50 43 61 41 46 58 69 46 47 80 78 61 59 74 0 0 0 3.225806 0 0 3.174603 0 0 3.125 0 2.439024 6.382979 6 0 1.639344

055 1 3 1 1 5 2 1 2 9 3 2 3 8 8 8 1 6 10 9 6 7 10 10 6 9 6 11 10 292 214 125 177 214 186 191 193 169 215 170 160 165 181 132 171 221 192 200 166 183 158 158 210 167 120 233 1.027397 0.46729 0.8 2.824859 0.934579 0.537634 1.04712 4.663212 1.775148 0.930233 1.764706 5 4.848485 4.41989 0.757576 3.508772

056 1 15 17 23 17 28 18 21 38 28 23 51 42 46 43 56 24 40 32 58 44 31 43 27 30 43 43 34 1045 967 636 762 892 645 715 749 733 776 665 601 584 632 547 562 548 587 530 479 467 457 425 421 512 547 605 1.435407 1.758014 3.616352 2.230971 3.139013 2.790698 2.937063 5.073431 3.819918 2.963918 7.669173 6.988353 7.876712 6.803797 10.23766 4.270463

057 1 0 2 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 18 16 8 8 21 9 20 13 10 33 21 16 10 20 31 23 17 14 24 9 16 9 27 29 31 23 30 0 12.5 0 0 14.28571 0 0 0 0 0 0 0 0 0 0 0

059 1 12 12 3 3 7 7 10 7 16 6 19 25 24 17 18 23 24 21 21 15 20 17 24 24 15 28 27 996 797 341 405 486 439 495 424 505 514 453 467 479 465 562 560 487 557 558 522 521 522 438 524 576 659 686 1.204819 1.505646 0.879765 0.740741 1.440329 1.594533 2.020202 1.650943 3.168317 1.167315 4.19426 5.353319 5.010438 3.655914 3.202847 4.107143

060 1 514 500 628 587 743 626 865 835 745 764 1032 1039 980 885 860 928 921 1018 1080 1024 944 882 1004 1030 1284 1289 1085 24703 24034 9715 10010 9934 10452 9782 10163 12192 12956 9408 10128 9178 8720 8606 8284 8341 8302 9021 8245 7717 7815 7606 7600 8574 8359 8981 2.080719 2.080386 6.464231 5.864136 7.479364 5.989284 8.842772 8.216078 6.110564 5.896882 10.96939 10.25869 10.67771 10.14908 9.993028 11.20232

063 1 40 43 35 36 14 29 29 35 27 27 26 31 25 28 16 16 16 16 19 29 15 18 15 24 35 38 22 1565 1233 552 440 461 487 396 498 583 607 423 455 481 594 538 515 460 475 459 480 373 342 384 374 462 450 425 2.555911 3.487429 6.34058 8.181818 3.036876 5.954825 7.323232 7.028112 4.631218 4.448105 6.146572 6.813187 5.197505 4.713805 2.973978 3.106796

064 1 133 142 144 148 143 140 167 159 120 141 141 136 140 113 69 47 47 43 59 52 44 78 74 91 101 102 121 3433 3216 1696 1636 1983 2093 1887 1980 1758 1781 1392 1448 1586 1474 1352 1446 1449 1281 1376 1168 1096 988 1009 1123 1094 1195 1265 3.874163 4.415423 8.490566 9.046455 7.211296 6.688963 8.850026 8.030303 6.825939 7.916901 10.12931 9.392265 8.827238 7.666214 5.10355 3.250346

068 1 40 23 36 31 55 39 52 51 46 43 39 38 29 32 20 23 20 19 22 30 27 31 24 43 39 26 23 1997 1467 680 652 654 664 689 648 702 661 613 566 458 585 505 561 510 469 415 412 390 389 397 452 526 486 549 2.003005 1.567825 5.294118 4.754601 8.409786 5.873494 7.54717 7.87037 6.552707 6.505295 6.362153 6.713781 6.331878 5.470085 3.960396 4.099822

069 1 2 3 1 3 2 2 2 11 2 5 7 5 21 9 6 5 11 21 17 5 7 5 9 7 18 20 11 571 775 491 451 356 481 422 469 464 446 298 468 455 348 329 489 403 460 397 390 300 344 382 344 478 512 566 0.350263 0.387097 0.203666 0.665188 0.561798 0.4158 0.473934 2.345416 0.431034 1.121076 2.348993 1.068376 4.615385 2.586207 1.823708 1.022495

070 1 0 0 4 0 3 7 3 7 3 8 5 10 7 3 4 7 5 1 2 4 3 3 2 5 5 8 11 352 328 296 280 235 289 290 385 358 300 204 227 178 326 380 357 347 237 244 316 343 331 371 551 553 518 608 0 0 1.351351 0 1.276596 2.422145 1.034483 1.818182 0.837989 2.666667 2.45098 4.405286 3.932584 0.920245 1.052632 1.960784

071 1 156 162 215 200 236 195 203 230 160 167 291 211 223 261 218 216 218 245 216 211 209 236 257 268 306 352 356 9723 9586 5117 3892 4306 4879 4934 4566 4411 4407 3082 3082 2749 2862 3068 2763 2622 2615 2562 2392 2241 2432 2564 3078 3235 3262 3382 1.604443 1.689965 4.201681 5.138746 5.480725 3.996721 4.114309 5.037232 3.627295 3.789426 9.441921 6.846204 8.112041 9.119497 7.105606 7.81759

072 1 19 20 11 9 13 10 6 9 14 5 23 6 12 10 6 8 6 17 6 7 5 17 12 13 10 22 10 555 817 438 412 352 334 322 308 509 505 269 305 303 263 321 278 296 360 310 269 306 277 305 343 266 317 232 3.423423 2.44798 2.511416 2.184466 3.693182 2.994012 1.863354 2.922078 2.750491 0.990099 8.550186 1.967213 3.960396 3.802281 1.869159 2.877698

074 1 14 36 32 34 47 35 22 26 31 27 20 28 36 16 21 23 21 27 31 26 18 18 21 23 28 19 27 776 1233 692 627 768 620 466 477 604 470 354 468 398 531 584 682 677 619 670 732 607 516 530 580 586 516 447 1.804124 2.919708 4.624277 5.422648 6.119792 5.645161 4.72103 5.450734 5.13245 5.744681 5.649718 5.982906 9.045226 3.013183 3.59589 3.372434

075 1 184 166 252 284 231 183 241 302 275 287 241 307 229 224 240 212 264 221 248 168 182 156 170 201 257 223 297 2526 3118 2842 2876 2408 2574 2971 3592 3365 3269 2427 2611 2220 2467 2369 2264 2244 2109 2178 2086 1890 2150 2174 2741 2494 2202 2527 7.284244 5.323926 8.866995 9.874826 9.593023 7.109557 8.111747 8.407572 8.172363 8.779443 9.929955 11.75795 10.31532 9.079854 10.13086 9.363958

To labour the point...

Page 44: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

New trends in visualization

• Widespread internet uptake has massively increased the availability of visualization technologies

• Open source toolkits are available for sophisticated analysis and visualization

• Emergence of the web as an analysis tool – the user only needs a browser to explore data, not expensive specialist software – “Web 2.0”

• Tools like Google Maps / Google Earth have brought spatial data visualization technologies into the public domain

Page 45: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Animated population pyramids(Creator: Martin Ralphs, Statistics NZ)

• Population Pyramids\NZ Dynamic Population Pyramid 1938-1990\index19381991.html

Page 46: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

A Visualisation Opportunity

• Use of commuting or migration flow data in raw form is cumbersome, if not impossible

• At Area Unit level, tables cannot be loaded into tools like Excel because of sheer size

• Linking web visualisation with a GIS (to provide the input data) we can give users a new way of interacting with these data

• Tools are low cost, customisable and (most importantly) RE-USABLE

• SVGFlowmap\CLICKME_TO_START.html

Page 47: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Standard Representation: The World by Land Mass Areahttp://www.worldmapper.org

Page 48: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Cartogram Representation: Proportion of GDP Spent on Military 2002http://www.worldmapper.org

Page 49: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Cartogram Representation: Population with Access to Affordable Drugshttp://www.worldmapper.org

Page 50: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Cartogram Representation: Households with Access to Sewerage Sanitationhttp://www.worldmapper.org

Page 51: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Cartogram Representation: Sulphur Dioxide Emissionshttp://www.worldmapper.org

Page 52: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Cartogram Representation: Species Extinctions Occurring 1500 - 2004http://www.worldmapper.org

Page 53: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Gapminder: www.gapminder.orgGeography, history, demography, econometrics(Creator: Hans Rosling)

http://www.gapminder.org

Page 54: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

What does all this mean?

• There’s never been a better time to visualize your data

• There have never been fewer excuses for NOT visualizing your data

• There has never been greater potential for misuse of visualization methods

• REMEMBER: If a visual looks slick and expensive, most people will assume it is correct.

Page 55: Using official statistics in the classroom Sharleen Forbes (assisted by Martin Ralph & Nathaniel Pihama) Statistics New Zealand School of Government, Victoria.

Questions and comments

Contact [email protected]

Thank you.