# NZC Level 1

# NZC Level 2

## Resources for teaching and learning

### Teacher Preparation

### Classroom Activities

### Tools

### Curriculum and Assessment

# NZC Level 3

## Resources for teaching and learning

### Key Resources

**Stick Figure Data Cards - Anna Fergusson****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Learning about the Census**

### Teacher Preparation

**Education and Training Census 2013 infographic****How Kids Learn – the statistical enquiry cycle****Statistical Investigation****STEW, STatistics Education Web****Alignment of C@S activities with National Standards****Building Statistical Thinking towards Level 6****Using the Data Viewer to explore stories in data.****Review of e-asTTle assessment tool: Statistics in the New Zealand Curriculum**

### Classroom Activities

**I notice, I wonder... - NCTM****By the Numbers: National Geographic Kids****Stick Figure Data Cards - Anna Fergusson****Nosey Parker 2****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Reconnecting Data and Chance****E-ako: Probability and Statistics Pathways****Conducting statistical investigations in Year 9 and Year 10 to develop learners’ statistical thinking****Misleading claims in the media: Junior focus****Engaging junior students in dynamic and collaborative statistics****Digital Learning Objects****Building Statistical Thinking towards Level 6****The Survey Toolkit****Nosey Parker 1****Stop or Dare****Collecting Data in the Classroom****Learning about the Census****Figure it Out****ID Cards**

### Tools

### Curriculum and Assessment

# NZC Level 4

## Resources for teaching and learning

### Key Resources

**Stick Figure Data Cards - Anna Fergusson****Masterpiece 2****Scatter it****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Statistical Reasoning with Data Cards - Webinar. Anna Fergusson****Year 9 and 10 Statistics and Probability****Posing summary investigative questions****Learning about the Census**

### Teacher Preparation

**Education and Training Census 2013 infographic****The Language of Shape****How Kids Learn – the statistical enquiry cycle****Statistical Investigation****Statistics Education 21st Century NZ****STEW, STatistics Education Web****Statistical Reasoning with Data Cards - Webinar. Anna Fergusson****Engaging Students in dynamic and collaborative Statistics****Alignment of C@S activities with National Standards****Building Statistical Thinking towards Level 6****Year 9 and 10 Statistics and Probability****Using the Data Viewer to explore stories in data.****Review of e-asTTle assessment tool: Statistics in the New Zealand Curriculum****Bowland Maths**

### Classroom Activities

**I notice, I wonder... - NCTM****By the Numbers: National Geographic Kids****Stick Figure Data Cards - Anna Fergusson****Canterbury Mathematics Association 2014 Statistics Teachers Day****Masterpiece 2****Scatter it****Interactive World Statistics****Making Stats more awesome - Helen Teal****The progression of Inference from Year 9 to AS1.10 and beyond****Nosey Parker 2****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Reconnecting Data and Chance****Mix'n'match statistical games****Data card sampling from a population Yr 9-12****E-ako: Probability and Statistics Pathways****Conducting statistical investigations in Year 9 and Year 10 to develop learners’ statistical thinking****How far until it stops?****Misleading claims in the media: Junior focus****Engaging junior students in dynamic and collaborative statistics****Oxfam: Bringing data to life****Engaging Students in dynamic and collaborative Statistics****Digital Learning Objects****Developing Quality in Mathematics Education (DQME)****Junior Statistics - an integrated programme (Year 9 and 10)****Building Statistical Thinking towards Level 6****Year 9 and 10 Statistics and Probability****Bowland Maths****The Survey Toolkit****Nosey Parker 1****8 glasses per day?****Statistical graphs and writing starters****Posing summary investigative questions****Stop or Dare****Collecting Data in the Classroom****Learning about the Census****Figure it Out****How high can you jump?****Speedster****Who wants to be a millionaire?****Using data cards****The case of the missing cake****Rumbling Tummy****Analysis tools**

### Tools

### Curriculum and Assessment

# NZC Level 5

## Resources for teaching and learning

### Key Resources

**Stick Figure Data Cards - Anna Fergusson****Caught in the path of the data deluge****Engaging with shape****Masterpiece 2****Masterpiece 3****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Karekare College: building conceptions of populations and samples****Introduction to making a call (Karekare College)****Developing Students' Inferential Reasoning****Animations of sampling variation****Developing the language of (statistical graphs) shape****Year 9 and 10 Statistics and Probability****Essential Teaching and Learning Experiences for successful Probabilistic Thinking****Probability experiences, Level 1 and before****Making the call Year 10****Learning about the Census**

### Teacher Preparation

**Caught in the path of the data deluge****Education and Training Census 2013 infographic****Using iNZight for the first time****The Language of Shape****How Kids Learn – the statistical enquiry cycle****Statistical Investigation****Animations of sampling variation****A teachers's guide to informal comparative reasoning****Statistics Education 21st Century NZ****STEW, STatistics Education Web****Engaging Students in dynamic and collaborative Statistics****Building Statistical Thinking towards Level 6****Developing the language of (statistical graphs) shape****Year 9 and 10 Statistics and Probability****Bowland Maths**

### Classroom Activities

**I notice, I wonder... - NCTM****Statistical thinking and reasoning for Level 1 - Dr Nic****By the Numbers: National Geographic Kids****Johnnie's Math Page - Probability****Activities for Probability - Pip Arnold****Stick Figure Data Cards - Anna Fergusson****2013 Census Spotlight on greater Christchurch****Engaging with shape****Canterbury Mathematics Association 2014 Statistics Teachers Day****Masterpiece 2****Masterpiece 3****Interactive World Statistics****Making Stats more awesome - Helen Teal****iNZight instructions 2 (Bear hugs 2)****Bear hugs 2****Armspans****The progression of Inference from Year 9 to AS1.10 and beyond****Nosey Parker 2****Bear hugs 3****iNZight instructions 1 (Bear Hugs 1)****Are you getting enough zzz?****Statistics Latte - Dru Rose****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Karekare College: building conceptions of populations and samples****Introduction to making a call (Karekare College)****Developing Students' Inferential Reasoning****iNZight instructions 3 (Bear hugs 3)****Data card sampling from a population Yr 9-12****E-ako: Probability and Statistics Pathways****How far until it stops?****Misleading claims in the media: Junior focus****Engaging junior students in dynamic and collaborative statistics****Oxfam: Bringing data to life****Engaging Students in dynamic and collaborative Statistics****Digital Learning Objects****Developing Quality in Mathematics Education (DQME)****Sugar guzzlers****Junior Statistics - an integrated programme (Year 9 and 10)****Building Statistical Thinking towards Level 6****Developing the language of (statistical graphs) shape****Year 9 and 10 Statistics and Probability****Bowland Maths****Junior Probability - Planning to learn****The Survey Toolkit****Nosey Parker 1****Statistical graphs and writing starters****Making the call Year 10****Learning about the Census****Masterpiece 1****Speedster****Statistical Investigations Part 3****Tell it like it is!****Cleaning data****A tall tale****Chocolicious****Big Foot****Bear Hugs 1****Statistical Investigations Part 2****Statistical Investigations Part 1: Introduction to the PPDAC cycle**

### Tools

### Curriculum and Assessment

# 1.10 Investigate a given multivariate data set using the statistical enquiry cycle

## Resources for teaching and learning

### Key Resources

**Guidelines for "How to make the call"****Videos: numeric-variables****Stick Figure Data Cards - Anna Fergusson****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Engaging with shape****Making the call Yr 11****Driven to Distraction Teaching Resource - Sarah Howell****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Karekare College: building conceptions of populations and samples****Introduction to making a call (Karekare College)****Developing Students' Inferential Reasoning****Sampling variation - developing big ideas for sample-to-population inferences****Sample to population inference - Michelle Dalrymple****Statistical Concepts Unpacked - Marion Steel****Video: Comparing Groups****Animations of sampling variation****Statistical Reasoning with Data Cards - Webinar. Anna Fergusson****Inference Pain Points - Robyn Headifen**

### Teacher Preparation

**Level 1 Standards Overview - Robyn Headifen****Guidelines for "How to make the call"****Videos: numeric-variables****Informal statistical inference revisited****Using iNZight for the first time****Success for all in NCEA Statistical Investigations****Changing Teaching Statistics: Real Data, Real learning****The Language of Shape****How Kids Learn – the statistical enquiry cycle****Statistical Investigation****Fitting data collection into Stats lessons - Jared Hockly****Sampling variation - developing big ideas for sample-to-population inferences****Sample to population inference - Michelle Dalrymple****Statistical Concepts Unpacked - Marion Steel****Video: Comparing Groups****Multivariate data FAQs****Animations of sampling variation****Building inferential reasoning in statistics Part 1****A teachers's guide to informal comparative reasoning****Laying the foundations for inference****Strategies and tools to support statistical report writing - Sophie Wright****Training teachers in statistical thinking****Approaches to sampling variability - Jared Hockly****Statistics Education 21st Century NZ****STEW, STatistics Education Web****Statistical Reasoning with Data Cards - Webinar. Anna Fergusson****Inference Pain Points - Robyn Headifen**

### Classroom Activities

**Statistical thinking and reasoning for Level 1 - Dr Nic****Stick Figure Data Cards - Anna Fergusson****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Engaging with shape****Making the call Yr 11****Driven to Distraction Teaching Resource - Sarah Howell****Armspans****Ready, steady, go****The progression of Inference from Year 9 to AS1.10 and beyond****Nosey Parker 2****Bear hugs 3****iNZight instructions 1 (Bear Hugs 1)****Sleeping Sheep****Are you getting enough zzz?****Statistics Latte - Dru Rose****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Karekare College: building conceptions of populations and samples****Introduction to making a call (Karekare College)****Developing Students' Inferential Reasoning****Baby Weights****Does Practice make perfect?****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****Mix'n'match statistical games****iNZight instructions 3 (Bear hugs 3)****How far until it stops?**

### Datasets

**CensusAtSchool 2007 data subset (15,000 rows)****CensusAtSchool 2009 data subset (15,000 rows)****NZ Incomes 2003 SURF**

### Tools

### Achievement Standard

# 1.11 Investigate bivariate numerical data using the statistical enquiry cycle

This standard is derived from Achievement Objective S6.1, plan and conduct surveys and experiments using the statistical enquiry cycle.

In particular,

- determine and justify appropriate variables and measures
- consider sources of variation
- gathering and cleaning data
- using multiple displays, and re-categorising data to find patterns and relationships, in multivariate data sets
- presenting a report of findings

The data must be numerical, with the explanatory variable (x variable) being either continuous or discrete, and the response variable (y variable) measured. The context of the data should be considered throughout the process.

## Achievement standard and Guides

- Achievement Standard (AS91036) Version 3 2015
- Conditions of Assessment (91036) Jan 2016
- Clarification of the standard (AS 91036)
- TKI Assessments
- Exemplars (AS91036)
- Senior Secondary Guide AO S6.1
- Key Ideas in Statistical Investigations

## Resources for teaching and learning

### Key Resources

**Masterpiece 2****Masterpiece 3****Scatter it****Video: Introduction to Relationships****Growing scatterplots****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Video: Trend, scatter and outliers [6:42]****Video: Relationships Between Numeric Variables [5 min]**

### Teacher Preparation

**Level 1 Standards Overview - Robyn Headifen****Statistical thinking in empirical enquiry****Using iNZight for the first time****Video: Introduction to Relationships****Success for all in NCEA Statistical Investigations****Changing Teaching Statistics: Real Data, Real learning****How Kids Learn – the statistical enquiry cycle****Statistical Investigation****Fitting data collection into Stats lessons - Jared Hockly****Video: Trend, scatter and outliers [6:42]****Video: Relationships Between Numeric Variables [5 min]****Training teachers in statistical thinking****Statistics Education 21st Century NZ****STEW, STatistics Education Web**

### Classroom Activities

**What's going on in this graph?****Masterpiece 2****Masterpiece 3****Scatter it****Interactive World Statistics****Using Gapminder Data to explore Bivariate data - Ricky Pedersen****Making Stats more awesome - Helen Teal****Making sense of the meaningful data all around us! - Michael Walden****iNZight instructions 2 (Bear hugs 2)****Bear hugs 2****Growing scatterplots****Nosey Parker 2****iNZight instructions 1 (Bear Hugs 1)****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Does Practice make perfect?****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****Mix'n'match statistical games****Oxfam: Bringing data to life**

### Datasets

**CensusAtSchool 2007 data subset (15,000 rows)****CensusAtSchool 2009 data subset (15,000 rows)****NZ Incomes 2003 SURF**

### Tools

### Achievement Standard

**Key Ideas in Statistical Investigations (Level 6)****Senior Secondary Guide AO S6.1****Exemplars (AS91036)****TKI Assessments****Clarification of the standard (AS 91036)****Conditions of Assessment (91036) Jan 2016****Achievement Standard (AS91036) Version 3 2015**

# 1.12 Demonstrate understanding of chance and data

This standard is derived from Achievement Objective S6.2, Evaluate statistical reports in the media by relating the displays, statistics, processes and probabilities to the claims made and S6.3, Investigate situations that involve elements of chance

- Calculating probabilities in discrete situations.

## Achievement standard and Guides

- Achievement Standard (AS91037)
- Assessment Specifications (AS91037) 2016
- Sample External assessments (AS91037)
- Senior Secondary Guide AO S6-2
- Senior Secondary Guide AO S6-3
- Glossary of Statistics terms

## Resources for teaching and learning

### Key Resources

**FigureNZ****Stats NZ Tatauranga Aotearoa****Stick Figure Data Cards - Anna Fergusson****Visualizing variation with Tinkerplots - Ruth Kaniuk****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Caught in the path of the data deluge****Response to the 2014 NZQA external assessments****Statistical literacy - Critical questions****Probability NCEA Level 1: Using TinkerPlots to aid the understanding of uncertainty**

### Teacher Preparation

**Reconnecting Chance and Data - Research: C. Konold & S. Kazak****Caught in the path of the data deluge****Response to the 2014 NZQA external assessments****Education and Training Census 2013 infographic****Statistical literacy - Critical questions****Changing Teaching Statistics: Real Data, Real learning****STEW, STatistics Education Web****Statistics NCEA external assessments 2013: feedback from NZSA Education Committee**

### Classroom Activities

**I notice, I wonder... - NCTM****Statistical thinking and reasoning for Level 1 - Dr Nic****What's going on in this graph?****Stick Figure Data Cards - Anna Fergusson****2013 Census Spotlight on greater Christchurch****Figure this -Resource website****Snapshots of New Zealand - Ki te ao mārama****Visualizing variation with Tinkerplots - Ruth Kaniuk****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Canterbury Mathematics Association 2014 Statistics Teachers Day****Relative Frequency****Sleeping Sheep****Data card sampling from a population Yr 9-12****Developing Quality in Mathematics Education (DQME)****Sunspots and Weather Correlations**

### Tools

### Sourcing Materials

### Achievement Standard

# 1.13 Investigate a situation involving elements of chance

## Resources for teaching and learning

### Key Resources

**Hands on activities for teaching risk - Lorraine O’Carroll****Visualizing variation with Tinkerplots - Ruth Kaniuk****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Essential Teaching and Learning Experiences for successful Probabilistic Thinking****Probability NCEA Level 1: Using TinkerPlots to aid the understanding of uncertainty****Probability distributions Level 5****Probability experiences, Level 1 and before**

### Teacher Preparation

**Level 1 Standards Overview - Robyn Headifen****Reconnecting Chance and Data - Research: C. Konold & S. Kazak****Changing Teaching Statistics: Real Data, Real learning****STEW, STatistics Education Web**

### Classroom Activities

**Hands on activities for teaching risk - Lorraine O’Carroll****Is this die fair?****Exploring paper, scissors, or rock****Quiz or no quiz****Exploring spinners****Sum of two dice****Johnnie's Math Page - Probability****Activities for Probability - Pip Arnold****How to train a dragon - Mary-Ellen Wilcox & Debra Leong****Visualizing variation with Tinkerplots - Ruth Kaniuk****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Canterbury Mathematics Association 2014 Statistics Teachers Day****Making sense of the meaningful data all around us! - Michael Walden****Relative Frequency**

### Sourcing Materials

### Achievement Standard

**Achievement Standard (AS91038) Version 3****Glossary of Statistics terms****Senior Secondary Guide AO S6-3****Key Ideas Probability Level 6****TKI Assessments (AS 91038)****Exemplars (AS 91038)****Clarification of the standard (AS91038)****Conditions of Assessment (AS91038) Jan 2016**

## Achievement standard and Guides

# 2.8 Design a questionnaire

## Resources for teaching and learning

### Key Resources

**Ethics in Statistics****Teaching research for NCEA L2 and L3 Statistics****StatsNZ: A guide to good survey design**

### Teacher Preparation

**Level 2 Standards Overview - Robyn Headifen****Ethics in Statistics****Teaching research for NCEA L2 and L3 Statistics****StatsNZ: A guide to good survey design****Survey Monkey - writing tips**

### Classroom Activities

**Questionnaires unit****Survey Monkey - Checklist****Social surveys: A history of resistance, scandal and negotiation****Questionnaire design**

### Tools

### Sourcing Materials

## Achievement Standard and Guides

# 2.9 Use statistical methods to make an inference

## Achievement standard and Guides

- Achievement Standard (AS91264) 2015
- Clarification of the Standard (AS91264)
- Conditions of assessment (AS91264) 2017
- TKI Assessments
- NZQA Annotated Exemplars
- Sample to population inference progressions
- Guidelines for “How to make the call”
- Standard overview and links (AS91264)

## Resources for teaching and learning

### Key Resources

**Guidelines for "How to make the call"****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Caught in the path of the data deluge****Engaging with shape****Sample to population inference - Michelle Dalrymple****Statistical Concepts Unpacked - Marion Steel****Video: Comparing Groups****Videos: Random error - the motivation for inference [7 min, 6 min]****Animations of sampling variation****Level 7 Statistical Investigations, Kiwi Kapers 1, 2 and 3****Teaching activities for AS 2.9 - Lindsay Smith****Visualising sampling variation at Level 7****FAQ for Level 2 Inference****Teaching research for NCEA L2 and L3 Statistics****Enriching sampling decisions in NCEA Level 2****Inference Pain Points - Robyn Headifen**

### Teacher Preparation

**Level 2 Standards Overview - Robyn Headifen****Guidelines for "How to make the call"****Caught in the path of the data deluge****Informal statistical inference revisited****Statistical thinking in empirical enquiry****Fitting data collection into Stats lessons - Jared Hockly****Sample to population inference - Michelle Dalrymple****Statistical Concepts Unpacked - Marion Steel****Video: Comparing Groups****Videos: Random error - the motivation for inference [7 min, 6 min]****Animations of sampling variation****Building inferential reasoning in statistics Part 1****A teachers's guide to informal comparative reasoning****Laying the foundations for inference****Issues in Level 2 NCEA: Use statistical methods to make an inference AS 91264****Strategies and tools to support statistical report writing - Sophie Wright****Telling Data Stories: Essential Dialogues for Comparative Reasoning****Training teachers in statistical thinking****Approaches to sampling variability - Jared Hockly****FAQ for Level 2 Inference****Statistics Education 21st Century NZ****Teaching research for NCEA L2 and L3 Statistics****Developing Statistical Literacy****Confidence Intervals developing big ideas - Dr Dalrymple's Blog****Inference Pain Points - Robyn Headifen**

### Classroom Activities

**Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Engaging with shape****Making sense of the meaningful data all around us! - Michael Walden****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****Mix'n'match statistical games****Level 7 Statistical Investigations, Kiwi Kapers 1, 2 and 3****Teaching activities for AS 2.9 - Lindsay Smith****iNZight instructions 3 (Bear hugs 3)****Property sales in North Shore city****Inference writing frame****To tag or not to tag?****Kiwi Kapers 1****Analysing student attendance data - Jason Ellwood****Data card sampling from a population Yr 9-12****Visualising sampling variation at Level 7****Enriching sampling decisions in NCEA Level 2**

### Datasets

**CensusAtSchool 2007 data subset (15,000 rows)****CensusAtSchool 2009 data subset (15,000 rows)****StatCrunch****SURF data sets****NZ Incomes 2003 SURF**

### Tools

# 2.10 Conduct an experiment to investigate a situation using statistical methods

## Achievement standard and Guides

- Achievement Standard (AS91265) 2015
- Clarification of the Standard (AS91265)
- Conditions of Assessment 2017
- TKI Assessments
- NZQA Annotated Exemplars
- Standard overview and links (AS91265)

## Resources for teaching and learning

### Key Resources

**Video: Randomised Experiments [5:24]****FAQ****Experiments at Level 7****Ethics in Statistics****Using Psychological Tests for the Experiments Standards****Teaching research for NCEA L2 and L3 Statistics****Fun and Practical Ideas for Level 2 and 3 Experiments: Michael Shadbolt****A brief introduction to experimental design**

### Teacher Preparation

**Level 2 Standards Overview - Robyn Headifen****Video: Randomised Experiments [5:24]****FAQ****Experiments at Level 7****Ethics in Statistics****Teaching research for NCEA L2 and L3 Statistics****What is an Experiment?****The basics of experimental design****Experimentation Glossary**

### Classroom Activities

**You can't fool me by giving me cheap cola!****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****Mix'n'match statistical games****AllTrials Project - Issues in health and medicine****Using Psychological Tests for the Experiments Standards****Fun and Practical Ideas for Level 2 and 3 Experiments: Michael Shadbolt**

### Tools

# 2.11 Evaluate a statistically based report

## Achievement standard and Guides

- Achievement Standard (AS91266) 2017
- Clarification of the standard (AS61266)
- Conditions of Assessment 2017
- Standard Overview and links (AS91266)
- TKI assessments
- NZQA exemplars

## Resources for teaching and learning

### Key Resources

**FigureNZ****Stats NZ Tatauranga Aotearoa****Videos: numeric-variables****Video: Introduction to Relationships****Statistical Concepts Unpacked - Marion Steel****Videos: Bad data****Teaching research for NCEA L2 and L3 Statistics****Enriching sampling decisions in NCEA Level 2****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Teaching Risk****STEW STatistics Education Web - Statistical Literacy resources**

### Teacher Preparation

**Videos: numeric-variables****Video: Introduction to Relationships****Statistical Concepts Unpacked - Marion Steel****Videos: Bad data****Talk back to statistics****StatsNZ Non-sampling errors****How to pass AS 91266****Teaching research for NCEA L2 and L3 Statistics****STEW STatistics Education Web - Statistical Literacy resources****Developing Statistical Literacy****All about election polls****Significant and reliable, Accuracy and Precision, Stats vocab****The median outclasses the mean**

### Classroom Activities

**What's going on in this graph?****Enriching sampling decisions in NCEA Level 2****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Teaching Risk****Statistical Reports from around the Pacific - Emma Mawby (Statistics NZ)****Movie issues: Crunching the data**

### Tools

### Sourcing Materials

# 2.12 Apply probability methods in solving problems

This standard is derived from Achievement Objectives S7.3, Evaluate statistically based reports, in particular, interpreting risk and relative risk,

and S7.4 Investigate situations that involve elements of chance.

In particular,

- comparing theoretical continuous distributions, such as the normal distribution, with experimental distributions
- calculating probabilities, using such tools as two-way tables and tree diagrams.

Using extended abstract thinking, students look at risk and probabilities in a wide range of contexts including statistics based reports or situations that involve elements of chance.

There are three parts to this standard,

Part A Interpreting risk and relative risk: They need to be able to calculate and interpret risk, select a baseline group, and calculate and interpret relative risk and absolute risk. Students should consider what relevant information may be missing.

Part B Compare theoretical distributions, such as the normal distribution, with experimental distributions. Students will describe and compare distributions and recognise when they have similar and different characteristics. Carry out an experimental investigation of probability situation and understand the ways a sample is likely to be representative of a population. Use the mean and standard deviation as sample statistics or as population parameters.

Part C Calculate probabilities, using tools such as two-way tables, probability trees. Students should be able to draw a probability tree based on a concrete situation including sampling with and without replacement. They can use probability trees to calculate simple conditional probabilities.

Where appropriate, use contextual knowledge to interpret and reflect on an answer generated by the above methods using appropriate statements.

## Achievement standard and Guides

- Achievement Standard (AS91267) 2015
- NZQA Exemplars, assessments and reports
- Assessment Specifications (AS91267) 2017
- Key Ideas in Probability
- Senior Secondary Guide AO S7-3
- Senior Secondary Guide AO S7-4
- Glossary of Statistics terms
- Level 2 Mathematics and Statistics Formulae (2016)

## Resources for teaching and learning

### Key Resources

**Visualizing variation with Tinkerplots - Ruth Kaniuk****Response to the 2014 NZQA external assessments****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Teaching Risk****Having fun with Probability Concepts and Solving Problems****Risk**

### Teacher Preparation

**Response to the 2014 NZQA external assessments****Developing Statistical Literacy****Risk****Statistics NCEA external assessments 2013: feedback from NZSA Education Committee****Risk in context – resources useful for teaching content related to AS 2.12****Risk**

### Classroom Activities

**Visualizing variation with Tinkerplots - Ruth Kaniuk****Canterbury Mathematics Association 2014 Statistics Teachers Day****Analysing student attendance data - Jason Ellwood****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Teaching Risk****Dependent and Independent events KHANAcademy****Probability: risk free****Using the Eikosogram to teach conditional and joint probability****Developing Quality in Mathematics Education (DQME)****Two way table practice****Legal blood alcohol****Drawing counters from a bag**

### Sourcing Materials

### Curriculum and Assessment

# 2.13 Investigate a situation involving elements of chance using a simulation

This standard is derived from Achievement Objective S7.4, Investigate situations that involve elements of chance, in particular, calculating probabilities using such tools as simulations and technology.

Students will show evidence of investigating the situation using each component of the simulation process, integrating statistical and contextual knowledge throughout the process.

Students will design the simulation for the given situation, identify the tools to be used, define what is a trial and the number of trials, determine the data recording methods; carry out the simulation and record the outcomes; select and use appropriate displays and measures; and communicate findings in a conclusion.

In their report the student should show evidence that they have:

- Designed the simulation for the situation given. They have described in detail the tools to be used, what a trial is, the number of trials and the data recording method. They have identified at least two assumptions in designing their simulation
- Conducted the initial simulation, recorded the results and repeated the simulation
- Selected and used appropriate displays and measures.

Students need to communicate their findings clearly, and link their recommendations clearly to the results of the simulation. They have discussed more than one aspect of the recommendation with respect to the context of the simulation in depth.

Note that the simulation can be done using technology (calculator or computer random numbers generated), and a record of the simulation must be set out in table form with labeled headings including the random numbers generated or selected.

## Achievement standard and Guides

- Achievement Standard (AS91268) 2015
- Clarification of the standard (AS91268)
- NZQA Exemplars, assessments and reports
- Key Ideas in Probability
- Senior Secondary Guide AO S7-4
- Glossary of Statistics terms

## Resources for teaching and learning

### Key Resources

**Hands on activities for teaching risk - Lorraine O’Carroll****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Teaching research for NCEA L2 and L3 Statistics****Stimulating simulations****A new world of simulations**

### Teacher Preparation

### Classroom Activities

**Hands on activities for teaching risk - Lorraine O’Carroll****Johnnie's Math Page - Probability****Activities for Probability - Pip Arnold****Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Canterbury Mathematics Association 2014 Statistics Teachers Day****Number of cereal packets****Understanding Probability****A new world of simulations****Benfold's law**

### Tools

### Sourcing Materials

# 3.8 Investigate time series data

## Resources for teaching and learning

### Key Resources

**Videos: Seasonal Decomposition and Forecasting [6 min + 5 min]****Teaching research for NCEA L2 and L3 Statistics****Selecting Time Series for teaching, learning and assessing****Time Series - from Achieved to Excellence****Statistical surprises and stories in time series data - Louise Addison****Video: Comparing Series [ 4 min]****Video: Introducing Time Series Data [4:38]****Suggestions for Teaching Time Series****Describing Trends - Statistics New Zealand**

### Teacher Preparation

**Level 3 Internal Standards overview - Robyn Headifen****Videos: Seasonal Decomposition and Forecasting [6 min + 5 min]****Strategies and tools to support statistical report writing - Sophie Wright****Teaching research for NCEA L2 and L3 Statistics****iNZight for beginners****Time Series: Managing the practical stuff****Careers in Statistics Posters****Video: Comparing Series [ 4 min]****Video: Introducing Time Series Data [4:38]****Suggestions for Teaching Time Series****Teacher's Guide to Holt Winters analysis****Time Series Analysis using iNZight**

### Classroom Activities

**Making sense of the meaningful data all around us! - Michael Walden****Measuring Price Change****Selecting Time Series for teaching, learning and assessing****TS Exercises for iNZight & iNZight Lite****Polar Ice Time Series Analysis****Time Series - from Achieved to Excellence****Sunspots and Weather Correlations****Statistical surprises and stories in time series data - Louise Addison****Going Paperless - David Knight****Describing Trends - Statistics New Zealand****Food Spending****iNZight Instructions for Time Series Analysis****Maths NZ Time Series Resources****Economic time series analysis****Hans Rosling: The good news of the decade?**

### Datasets

**15 Time Series Datasets (2012)****Time Series Data 2017****Times Series Data Library****NZ Visitor Arrivals (Quarterly)****NZ Visitor Arrivals (Monthly)****NZ Visitor Numbers (Monthly)****NZ Visitor Numbers (Quarterly)****Statistics New Zealand Time Series Datasets****Food Spending****Time Series Datasets (2013)****Box Office Dataset**

### Tools

### Achievement Standard

# 3.9 Investigate bivariate measurement data

## FAQ

**Why isn't "interpretation of the slope in context" in the 3.9 standard?****Can we use iNZight to work out residuals and draw residual plots?**

## Resources for teaching and learning

### Key Resources

**Video: Introduction to Relationships****Video: Trend, scatter and outliers [6:42]****Video: Relationships Between Numeric Variables [5 min]****Ethics in Statistics****Teaching research for NCEA L2 and L3 Statistics****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Statistical surprises and stories in bivariate data - Louise Addison****Aiming for Excellence in bivariate data****Article: Interpreting the slope of a trend line****Article: Association and correlation****Videos: Some next steps****Video: More about Relationships [1:32]****Video: Lines, curves and smoothers [4 min]****McDonald's food nutritional study****Investigating bivariate measurement data using iNZight**

### Teacher Preparation

**Level 3 Internal Standards overview - Robyn Headifen****Video: Introduction to Relationships****Video: Trend, scatter and outliers [6:42]****Video: Relationships Between Numeric Variables [5 min]****Strategies and tools to support statistical report writing - Sophie Wright****Ethics in Statistics****Teaching research for NCEA L2 and L3 Statistics****Article: Interpreting the slope of a trend line****Article: Association and correlation****Videos: Some next steps****Video: More about Relationships [1:32]****Careers in Statistics Posters****Video: Lines, curves and smoothers [4 min]****Investigating bivariate measurement data using iNZight****Genstat for Yr 11 and 13 Statistical analysis****Regression**

### Classroom Activities

**Analysing student attendance data - Jason Ellwood****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Data Journalism****Statistical surprises and stories in bivariate data - Louise Addison****Aiming for Excellence in bivariate data****Maui's dolphin: uncovering a new sub-species****Against All Odds - Scatterplot unit****McDonald's food nutritional study****Dead men DO Tell Tales and other Statistical Stories****Investigating the relationship between the weight of cars and their fuel efficiency****Meaningless and meaningful correlations****Fitness levels****200 countries in 200 years****Hans Rosling: The good news of the decade?**

### Datasets

**Data sets for bivariate investigations****CensusAtSchool 2007 data subset (15,000 rows)****CensusAtSchool 2009 data subset (15,000 rows)****SURF data sets****NZ Incomes 2003 SURF****Journal of Statistics Education - Datasets**

### Tools

### Achievement Standard

# 3.10 Use statistical methods to make a formal inference

# 3.11 Conduct an experiment to investigate a situation using experimental design principles

## Resources for teaching and learning

### Key Resources

**Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****Experiments and the Randomisation Test****Next Steps****Video: Randomisation Test [7:45]****Video: Randomisation Variation [6:01]****Video: Randomised Experiments [5:24]****Ethics in Statistics****Using Psychological Tests for the Experiments Standards****Teaching research for NCEA L2 and L3 Statistics****Experimental units that are not physical entities****Why do randomisation tests in the experiments standards****FAQ****Tips on critiquing causal-relationship claims****Conducting Experiments: Workbook for Students****Introduction to Randomisation****Star Trek Inference Tour****Water taste Testing****Memory test****Fun and Practical Ideas for Level 2 and 3 Experiments: Michael Shadbolt****Animations for teaching bootstrapping and randomisation****Getting started on VIT modules in iNZight VIT****Conducting and assessing experiments for 3.11****A guide to the randomisation test****A brief introduction to experimental design**

### Teacher Preparation

**Level 3 Internal Standards overview - Robyn Headifen****Experiments and the Randomisation Test****Next Steps****Video: Randomisation Test [7:45]****Video: Randomisation Variation [6:01]****Video: Randomised Experiments [5:24]****Ethics in Statistics****Teaching research for NCEA L2 and L3 Statistics****Why do randomisation tests in the experiments standards****FAQ****Tips on critiquing causal-relationship claims****Introduction to Randomisation****Dynamic Visualizations for Inference****What is an Experiment?****National Newsletter, Term 4, 2012****Curriculum Level 8 Experiments - A classroom review****The basics of experimental design****Experimentation Glossary****Star Trek Inference Tour****Statistical Experiments and Design****Animations for teaching bootstrapping and randomisation****Changing Needs in a Changing World**

### Classroom Activities

**Sampling variation just keeps turning up everywhere! - Michelle Dalrymple****AllTrials Project - Issues in health and medicine****Using Psychological Tests for the Experiments Standards****Experimental units that are not physical entities****Statistical Experiments MathsNZ****Conducting Experiments: Workbook for Students****Water taste Testing****Memory test****Fun and Practical Ideas for Level 2 and 3 Experiments: Michael Shadbolt****Hatching success of the Takahe****Critical Skills, Concepts and Techniques for Level 3 Experiments****Getting started on VIT modules in iNZight VIT****Animal welfare**

### Tools

### Achievement Standard

**Achievement Standard 3.11 (AS91583)****NZQA Clarification of the standard (AS91583)****Conditions of assessment (AS91583) Jan 2017****NZQA Exemplars (AS91583)****TKI assessments****Related Achievement Objectives 8.1 & 8.2**

# 3.12 Evaluate statistically based reports

## Resources for teaching and learning

### Key Resources

**FigureNZ****Stats NZ Tatauranga Aotearoa****Hands on activities for teaching risk - Lorraine O’Carroll****Caught in the path of the data deluge****Response to the 2014 NZQA external assessments****Statistical Concepts Unpacked - Marion Steel****Resources for the "big ideas" behind Statistical reports****Videos: Bad data****FAQs for Inferential thinking****Teaching research for NCEA L2 and L3 Statistics****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Teaching Risk****STEW STatistics Education Web - Statistical Literacy resources****Margin of Error and testing claims in the media****Margin of Error: Clarifying the rules of Thumb****Article: Confidence intervals – What matters most?****Teaching Level 3 Statistical Reports: How are we doing?****Higher level communication for Scholarship and Excellence****Non-Sampling Errors as they Apply to Polls & Surveys and Experiments & Observational Studies****Tips on critiquing causal-relationship claims**

### Teacher Preparation

**Caught in the path of the data deluge****Response to the 2014 NZQA external assessments****Statistical Concepts Unpacked - Marion Steel****Resources for the "big ideas" behind Statistical reports****Videos: Bad data****FAQs for Inferential thinking****Teaching research for NCEA L2 and L3 Statistics****STEW STatistics Education Web - Statistical Literacy resources****Developing Statistical Literacy****All about election polls****Significant and reliable, Accuracy and Precision, Stats vocab****Margin of Error and testing claims in the media****The median outclasses the mean****Margin of Error: Clarifying the rules of Thumb****Article: Confidence intervals – What matters most?****Understanding Big Data****Statistics NCEA external assessments 2013: feedback from NZSA Education Committee****Non-Sampling Errors as they Apply to Polls & Surveys and Experiments & Observational Studies****Tips on critiquing causal-relationship claims**

### Classroom Activities

**What's going on in this graph?****Hands on activities for teaching risk - Lorraine O’Carroll****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Teaching Risk****Margin of Error and testing claims in the media****Visualising chance: A pilot study at the introductory level (Senior secondary/Tertiary)****Inference for Proportions and Inference for a Population****3.12 Practice Assessment****Margin of error in media reports****What can I do with a degree in Statistics?****Margin of Error****Teaching Level 3 Statistical Reports: How are we doing?****Level 3 Statistically based reports - Dru Rose****Statistical Reports from around the Pacific - Emma Mawby (Statistics NZ)****Data Journalism****Rock 'n Poll****The predictive power of polls****Movie issues: Crunching the data**

### Tools

### Sourcing Materials

**FigureNZ****Stats NZ Tatauranga Aotearoa****Health studies****Bad science****OECD data****Significance Magazine****International Statistical Literacy Project****Friends Bully More Than Enemies - Research****Numeracy in the News****Chance news****More or Less: Behind the Stats****StatsChat****Stats+Stories**

### Achievement Standard

**Achievement Standard 3.12 (91584)****FORMULAE AND TABLES BOOKLET for 91584 (2016)****NZQA assessments, reports and schedules****Assessment Specifications (AS91584)****Related Achievement Objectives 8.1, 8.2 & 8.3**

# 3.13 Apply probability concepts in solving problems

This standard is derived from Achievement Objective S8.4, Investigate situations that involve elements of chance.

- calculating probabilities of independent, combined and conditional events

Students should be able to:

- Understand true probability vs model estimates vs experimental estimates
- Randomness, independence mutually exclusive events, conditional probability
- Probability distribution tables and graphs
- Two way tables, probability tress, venn diagrams

This standard requires students to understand the relationship between true probability, model estimates, and experimental estimates.

## Achievement standard and Guides

- Achievement Standard 3.13 (AS 91585)
- NZQA Exemplars, assessments and reports
- Assessment Specifications (AS91585) 2016
- Moderator’s Newsletter
- Key Ideas in Probability
- Senior Secondary Guide AO S8-4
- Glossary of Statistics terms
- Level 3 Statistics Formulae 2013

## FAQ

## Resources for teaching and learning

### Key Resources

**Hands on activities for teaching risk - Lorraine O’Carroll****Response to the 2014 NZQA external assessments****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Having fun with Probability Concepts and Solving Problems****Risk****Higher level communication for Scholarship and Excellence****Statistical surprises and stories - Probability Louise Addison****Probability NCEA Level 1: Using TinkerPlots to aid the understanding of uncertainty****Using Tinkerplots for probability modelling**

### Teacher Preparation

**Response to the 2014 NZQA external assessments****Risk****Statistics NCEA external assessments 2013: feedback from NZSA Education Committee****Some probability teaching ideas****Apply probability concepts in solving problems****Deterministic and Probabilistic Models****Venn Diagrams****Understanding true probability, model estimates, and experimental estimates**

### Classroom Activities

**Hands on activities for teaching risk - Lorraine O’Carroll****Canterbury Mathematics Association 2014 Statistics Teachers Day****Analysing student attendance data - Jason Ellwood****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Visualising chance: A pilot study at the introductory level (Senior secondary/Tertiary)****What can I do with a degree in Statistics?****Using the Eikosogram to teach conditional and joint probability****Two way table practice****Statistical surprises and stories - Probability Louise Addison****Some probability teaching ideas****Interactive Probability quiz****Conditional Probability Visualisation****Understanding Probability****Classic problems in Probability****Senior Secondary Guides - Teaching and Learning Activities****Calculating probabilities of independent, combined and conditional events**

### Sourcing Materials

# 3.14 Apply probability distributions in solving problems

This standard is derived from Achievement Objective S8.4, Investigate situations that involve elements of chance.

- calculating and interpreting expected values and standard deviations of discrete random variables
- applying distributions such as the Poisson, binomial and normal

Methods are selected from those related to:

- discrete and continuous probability distributions
- mean and standard deviation of random variables
- distribution of true probabilities versus distribution of model estimates of probabilities versus distribution of experimental estimates of probabilities.

Students should be able to calculate the mean and standard deviation from a plot of the distribution of a discrete random variable, linking probabilities and areas under density functions for continuous outcomes.

## Achievement standard and Guides

- Achievement Standard 3.14 (AS 91586)
- NZQA Exemplars, assessments and reports
- Assessment Specifications (AS91586) 2016
- Moderator’s Newsletter
- Key Ideas in Probability
- Senior Secondary Guide AO S8-4
- Glossary of Statistics terms
- Level 3 Statistics Formulae 2013

## FAQ

## Resources for teaching and learning

### Key Resources

**Response to the 2014 NZQA external assessments****Higher level communication for Scholarship and Excellence****Probability distributions - What are the big ideas and how do we effectively teach them?****Probability NCEA Level 1: Using TinkerPlots to aid the understanding of uncertainty****Distribution of true probabilities and other new ideas**

### Teacher Preparation

**Response to the 2014 NZQA external assessments****All models are wrong, but some are more wrong than others - Anna Martin****Statistics NCEA external assessments 2013: feedback from NZSA Education Committee****Apply probability distributions in solving problems****Deterministic and Probabilistic Models****Understanding true probability, model estimates, and experimental estimates****Probability distributions - What are the big ideas and how do we effectively teach them?****A note on Poisson model assumptions**

### Classroom Activities

**Canterbury Mathematics Association 2014 Statistics Teachers Day****Visualising chance: A pilot study at the introductory level (Senior secondary/Tertiary)****What can I do with a degree in Statistics?****Developing Quality in Mathematics Education (DQME)****Triangular distribution notes and resources****Statistical surprises and stories Probability distributions - Louise Addison****Probability distributions - What are the big ideas and how do we effectively teach them?****Conditional Probability Visualisation****Senior Secondary Guides - Teaching and Learning Activity****Expected value and standard deviation of discrete random variables****Student exemplars for distributions****Too many boys?****Fillings**

### Sourcing Materials

# Scholarship

Scholarship Statistics candidates are expected to demonstrate high-level critical thinking, abstraction and generalisation, and to integrate, synthesise and apply knowledge, skills, understanding and ideas to complex situations.

The student will use knowledge of statistics to apply statistical and probability concepts and methods to complex problems in contexts which may be unfamiliar, interpret and, where appropriate, make inferences and clearly communicate concepts and findings.

* Applying* and *interpreting *statistical and probability concepts and methods may involve:

- exploring data
- drawing on informed contextual knowledge
- making inferences
- dealing with sources and consequences of uncertainty
- applying appropriate models
- stating and evaluating assumptions of models used
- explaining conceptions and processes (e.g. simulation-based processes)
- critiquing based on the Problem-Plan-Data-Analysis-Conclusion (PPDAC) cycle
- offering competing explanations and important follow-up questions
- evaluating statistically based and / or probabilistically based reports

* * from the NZQA Statistics Performance Standard*

**Scholarship Statistics Specifications and Guides**

- NZQA Scholarship Awards
- Statistics Assessment Specification and Examinations 2013 – 2004
- Statistics Scholarship Performance Standard Dec 12
- Sample Resources
- Some personal comments on the NZ Scholarship Statistics Sample Examination

## Resources for teaching and learning

### Key Resources

### Teacher Preparation

**2016 Panel discussion on Scholarship Statistics****2015 Scholarship Statistics discussion group****Video: Comparing Series [ 4 min]**