# NZC Level 1

# NZC Level 2

## Resources for teaching and learning

### Teacher Preparation

### Classroom Activities

### Curriculum and Assessment

# NZC Level 3

## Resources for teaching and learning

### Key Resources

### Teacher Preparation

**STEW, STatistics Education Web****Education and Training Census 2013 infographic****Statistical Investigation****How Kids Learn – the statistical enquiry cycle****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

**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****Reconnecting Data and Chance****The Survey Toolkit****Stick Figure Data Cards****Nosey Parker 1****Nosey Parker 2****Stop or Dare****Collecting Data in the Classroom****Learning about the Census****Figure it Out****ID Cards**

### Curriculum and Assessment

# NZC Level 4

## Resources for teaching and learning

### Key Resources

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

### Teacher Preparation

**Statistical Reasoning with Data Cards - Webinar. Anna Fergusson****STEW, STatistics Education Web****Engaging Students in dynamic and collaborative Statistics****Statistics Education 21st Century NZ****Education and Training Census 2013 infographic****Statistical Investigation****How Kids Learn – the statistical enquiry cycle****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****The Language of Shape**

### Classroom Activities

**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****Reconnecting Data and Chance****The Survey Toolkit****Stick Figure Data Cards****Canterbury Mathematics Association 2014 Statistics Teachers Day****Nosey Parker 1****8 glasses per day?****Nosey Parker 2****Statistical graphs and writing starters****Posing summary investigative questions****Data card sampling from a population Yr 9-12****Stop or Dare****Collecting Data in the Classroom****Learning about the Census****The progression of Inference from Year 9 to AS1.10 and beyond****Figure it Out****How high can you jump?****Speedster****Masterpiece 2****Who wants to be a millionaire?****Using data cards****The case of the missing cake****Scatter it****Rumbling Tummy****Analysis tools**

### Tools

### Sourcing Materials

### Curriculum and Assessment

**Making stats more awesome - moving towards student centred learning****Alignment of C@S activities with National Standards****Review of e-asTTle assessment tool: Statistics in the New Zealand Curriculum****Unit Planning for Junior Statistics and Probability****Canterbury Mathematics Association 2014 Statistics Teachers Day**

# NZC Level 5

## Resources for teaching and learning

### Key Resources

**Animations of sampling variation****Developing the language of (statistical graphs) shape****Year 9 and 10 Statistics and Probability****Developing Students' Inferential Reasoning****Karekare College: building conceptions of populations and samples****Introduction to making a call****Essential Teaching and Learning Experiences for successful Probabilistic Thinking****Probability experiences, Level 1 and before****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster****Making the call Year 10****Learning about the Census**

### Teacher Preparation

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

### Classroom Activities

**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)****Statistics Latte****Are you getting enough zzz?****Building Statistical Thinking towards Level 6****Developing the language of (statistical graphs) shape****Year 9 and 10 Statistics and Probability****Bowland Maths****Johnnie's Math Page - Probability****Junior Probability - Planning to learn****The Survey Toolkit****iNZight instructions 3 (Bear hugs 3)****iNZight instructions 1 (Bear Hugs 1)****iNZight instructions 2 (Bear hugs 2)****Bear hugs 2****Bear hugs 3****2013 Census Spotlight on greater Christchurch****Stick Figure Data Cards****Engaging with shape****Canterbury Mathematics Association 2014 Statistics Teachers Day****Nosey Parker 1****Nosey Parker 2****Statistical graphs and writing starters****Making the call Year 10****Data card sampling from a population Yr 9-12****Activities for Probability****Learning about the Census****The progression of Inference from Year 9 to AS1.10 and beyond****Masterpiece 1****Speedster****Masterpiece 2****Masterpiece 3****Statistical Investigations Part 3****Tell it like it is!****Cleaning data****Armspans****A tall tale****Chocolicious****Big Foot****Bear Hugs 1****Statistical Investigations Part 2****Statistical Investigations Part 1: Introduction to the PPDAC cycle**

### Tools

### Sourcing Materials

### Curriculum and Assessment

# 1.10 Investigate a given multivariate data set 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
- cleaning data
- using multiple data displays, and re-categorising data to find patterns, variations, in multivariate data sets.
- comparing sample distributions visually, using measures of centre, spread, and proportion
- presenting a report of findings.

It is important for students to consider the context of the data and make an informal inference about the population from the sample data.

## Achievement standard and Guides

- Achievement Standard (AS91035)
- Conditions of Assessment (AS91035) Jan 2016
- Clarification of the standard (AS91035)
- TKI Assessments (AS91035)
- Exemplars (AS91035)
- Moderator’s newsletter comments regarding posing comparative questions July 2012
- Senior Secondary Guide AO S6.1
- Sample to population inference progressions
- Key Ideas in Statistical Investigations
- Glossary of statistics terms

## FAQ

**What possible relevance can statements about the sample be in helping us draw a conclusion about the population?****Can we make the assumption that C@S data is a population?**

## Resources for teaching and learning

### Key Resources

**Statistical Reasoning with Data Cards - Webinar. Anna Fergusson****Sample to population inference - The Path to 3.10****Sampling variation - developing big ideas with sample-to-population inferences****Inference Pain Points - Robyn Headifen****Animations of sampling variation****Guidelines for "How to make the call"****Developing Students' Inferential Reasoning****Karekare College: building conceptions of populations and samples****Introduction to making a call****Driven to Distraction Unit Resource****Te Tūhuratanga Tauanga He Toa Tūhura Koe****Data Detective Poster**

### Teacher Preparation

**Statistical Reasoning with Data Cards - Webinar. Anna Fergusson****Statistical Concepts Unpacked****STEW, STatistics Education Web****Strategies, tools and prompts to support statistical report writing****Fitting data collection into your Stats lessons****Sample to population inference - The Path to 3.10****Sampling variation - developing big ideas with sample-to-population inferences****Inference Pain Points - Robyn Headifen****Animations of sampling variation****Statistics Education 21st Century NZ****Building inferential reasoning in statistics Part 1****A teachers's guide to informal comparative reasoning****Laying the foundations for inference****Statistical Investigation****How Kids Learn – the statistical enquiry cycle****Using iNZight for the first time****Year 11 Success for all in NCEA Statistical Investigations****Changing Teaching Statistics: Real Data, Real learning****Level 1 Standards Overview****Difficulties in learning about sampling variability, and teacher approaches to overcome these****Guidelines for "How to make the call"****The Language of Shape****Training teachers in statistical thinking**

### Classroom Activities

**How far until it stops?****Sampling variation just keeps turning up everywhere!****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****Statistics Latte****Are you getting enough zzz?****iNZight instructions 3 (Bear hugs 3)****iNZight instructions 1 (Bear Hugs 1)****Sleeping Sheep****Informal statistical inference revisited****Bear hugs 3****Stick Figure Data Cards****Engaging with shape****Making the call Yr 11****Nosey Parker 2****The progression of Inference from Year 9 to AS1.10 and beyond****Ready, steady, go****Armspans****Does Practice make perfect?****Baby Weights****You can't fool me by giving me cheap cola!**

### Datasets

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

### Tools

# 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
- Glossary of Statistics terms

## Resources for teaching and learning

### Key Resources

### Teacher Preparation

**STEW, STatistics Education Web****Fitting data collection into your Stats lessons****Statistics Education 21st Century NZ****Statistical Investigation****How Kids Learn – the statistical enquiry cycle****Using iNZight for the first time****Year 11 Success for all in NCEA Statistical Investigations****Changing Teaching Statistics: Real Data, Real learning****Level 1 Standards Overview****Statistical thinking in empirical theory****Training teachers in statistical thinking**

### Classroom Activities

**Making sense of the meaningful data all around us!****Oxfam: Bringing data to life****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****iNZight instructions 1 (Bear Hugs 1)****iNZight instructions 2 (Bear hugs 2)****Bear hugs 2****Nosey Parker 2****Growing scatterplots****Masterpiece 2****Masterpiece 3****Scatter it****Does Practice make perfect?**

### Datasets

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

### Tools

### Sourcing Materials

### Curriculum and Assessment

# 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

**Statistical literacy critical questions****Visualizing variation with Tinkerplots****Probability NCEA Level 1: Using TinkerPlots to aid the understanding of uncertainty**

### Teacher Preparation

**Response to the 2014 NZQA external assessments****Developing Statistical Literacy****Statistics NCEA external assessments 2013: feedback from NZSA Education Committee****STEW, STatistics Education Web****Caught in the path of the data deluge****Education and Training Census 2013 infographic****Statistical literacy critical questions****Using critical questions to evaluate an article****Changing Teaching Statistics: Real Data, Real learning**

### Classroom Activities

**Sampling variation just keeps turning up everywhere!****Developing Quality in Mathematics Education (DQME)****Sunspots and Weather Correlations****Using critical questions to evaluate an article****Figure this****Snapshots of New Zealand - Ki te ao mārama****2013 Census Spotlight on greater Christchurch****Stick Figure Data Cards****Canterbury Mathematics Association 2014 Statistics Teachers Day****Data card sampling from a population Yr 9-12**

### Tools

### Sourcing Materials

### Curriculum and Assessment

# 1.13 Investigate a situation involving elements of chance

This standard is derived from Achievement Objective S6.3 Investigate situations that involve elements of chance.

This standard encourages students to undertake a probability experiment. They will need to pose a question, plan and conduct an experiment, choose appropriate displays including experimental probability distributions, and identify and communicate patterns in the data. Students need to understand the variation between theoretical and experimental probability distributions and realise the effect of the sample size.

## Achievement standard and Guides

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

## Resources for teaching and learning

### Key Resources

**Hands on activities for teaching risk****Essential Teaching and Learning Experiences for successful Probabilistic Thinking****Visualizing variation with Tinkerplots****Probability NCEA Level 1: Using TinkerPlots to aid the understanding of uncertainty****Probability distributions Level 5****Probability experiences, Level 1 and before**

### Teacher Preparation

**STEW, STatistics Education Web****Changing Teaching Statistics: Real Data, Real learning****Level 1 Standards Overview**

### Classroom Activities

**Hands on activities for teaching risk****Making sense of the meaningful data all around us!****Sampling variation just keeps turning up everywhere!****Johnnie's Math Page - Probability****How to train a dragon AS91038 Practice Task****Canterbury Mathematics Association 2014 Statistics Teachers Day****Exploring paper, scissors, or rock****Activities for Probability****Exploring spinners****Quiz or no quiz****Sum of two dice****Is this die fair?**

### Sourcing Materials

### Curriculum and Assessment

# 2.8 Design a questionnaire

## Resources for teaching and learning

### Key Resources

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

### Teacher Preparation

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

### Classroom Activities

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

### Tools

### Sourcing Materials

## Achievement Standard and Guides

# 2.9 Use statistical methods to make an inference

This internal Achievement Standard is derived from Achievement Objective S7.1, Carry out investigations using the statistical enquiry cycle.

In particular, using existing data sets,

- evaluating the choice of sampling and data collection methods used
- using relevant contextual knowledge, exploratory data analysis, and statistical inference,

and S7.2, Make inferences from surveys,

- using sample statistics to make point estimates of population parameters
- recognising the effect of sample size on the variability of an estimate.

Using an existing data set of population data, students will pose an investigative comparison question, select random samples, use appropriate displays and measures, discuss sampling distributions and variability including the variability of estimates. They will use sample statistics to make point estimates of population parameters and make an inference. Attention should be paid to the shape of sampling distributions and whether or not samples overlap. It is important throughout the statistical enquiry cycle to consider the context of the data.

Note,

- statistical inference – the process of drawing conclusions about population parameters based on a sample taken from the population.
- sampling error – the error caused because data are collected from part of population (even if a sample is unbiased), rather than the whole population.

## Achievement standard and Guides

- Achievement Standard (AS91264) 2015
- NZQA Exemplars, assessments and reports
- Clarification of the Standard (AS91264)
- Conditions of assessment
- Moderator’s newsletter comments regarding posing comparative questions July 2012
- Senior Secondary Guide AO S7-1
- Senior Secondary Guide AO S7-2
- Sample to population inference progressions
- Guidelines for “How to make the call”
- Key Ideas in Statistical Literacy
- Glossary of Statistics terms

## FAQ

**Kiwi Kapers, I wonder what is the median weight of kiwis? How should I encourage my students to write conclusions when making an inference?****Can you please clarify the definition of a sampling error as students often get confused between sampling error and non-sampling error?****How do I correctly pose a comparison investigative question for Kiwi Kapers 3 and state my conclusions when making an inference about the population?****Why have there been so many changes to the Statistics Curriculum, especially with regards to the Central Limit Theorem and Confidence Intervals?****What is the name of the error bounds for the sample median?****What possible relevance can statements about the sample be in helping us draw a conclusion about the population?****Can we make the assumption that C@S data is a population?**

## Resources for teaching and learning

### Key Resources

**Teaching research for NCEA L2 and L3 Statistics****Sample to population inference - The Path to 3.10****Level 7 Statistical Investigations, Kiwi Kapers 1, 2 and 3****Inference Pain Points - Robyn Headifen****FAQs for Inferential thinking****Animations of sampling variation****Visualising sampling variation at Level 7****Guidelines for "How to make the call"**

### Teacher Preparation

**Level 2 Standards Overview****Teaching research for NCEA L2 and L3 Statistics****Developing Statistical Literacy****Statistical Concepts Unpacked****Strategies, tools and prompts to support statistical report writing****Fitting data collection into your Stats lessons****Sample to population inference - The Path to 3.10****Confidence Intervals developing big ideas - Dr Dalrymple's Blog****Inference Pain Points - Robyn Headifen****FAQs for Inferential thinking****Animations of sampling variation****Caught in the path of the data deluge****Statistics Education 21st Century NZ****Building inferential reasoning in statistics Part 1****A teachers's guide to informal comparative reasoning****Laying the foundations for inference****Teaching activities for Achievement Standard 2.9****Difficulties in learning about sampling variability, and teacher approaches to overcome these****Visualising sampling variation at Level 7****Issues in Level 2 NCEA: Use statistical methods to make an inference AS 91264****Guidelines for "How to make the call"****Statistical thinking in empirical theory****Training teachers in statistical thinking****Telling Data Stories: Essential Dialogues for Comparative Reasoning**

### Classroom Activities

**Enriching sampling decisions in NCEA Level 2****Making sense of the meaningful data all around us!****Sampling variation just keeps turning up everywhere!****Analysing Student Attendance Data****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards****Level 7 Statistical Investigations, Kiwi Kapers 1, 2 and 3****Teaching activities for Achievement Standard 2.9****Visualising sampling variation at Level 7****iNZight instructions 3 (Bear hugs 3)****Finding Informal Confidence Intervals****Informal statistical inference revisited****Property sales in North Shore city****Engaging with shape****Data card sampling from a population Yr 9-12****Inference writing frame****Kiwi Kapers 1****To tag or not to tag?**

### Datasets

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

### Tools

### Curriculum and Assessment

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

This standard is derived from Achievement Objectives S7.1, Carry out investigations of phenomena using the statistical enquiry cycle.

In particular,

- conducting experiments
- evaluating the choice of measures for variables and data collection methods used
- using relevant contextual knowledge, exploratory data analysis, and statistical inference.

Evidence of each step of the statistical enquiry cycle should be documented. This process includes posing an investigative question, plan and conduct the experiment, select appropriate displays and measures, discuss findings in a conclusion, supporting findings with evidence gained from the experiment. Note that an experiment requires an intervention and cannot be an observation study.

Experiments can be either,

- Two independent group comparison, or
- Paired comparisons.

## Achievement standard and Guides

- Achievement Standard (AS91265) 2015
- Clarification of the Standard (AS91265)
- NZQA Exemplars, assessments and reports
- Key Ideas in Statistical Investigations
- Senior Secondary Guide AO S7-1
- Glossary of Statistics terms

## FAQ

## Resources for teaching and learning

### Key Resources

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

### Teacher Preparation

**Level 2 Standards Overview****Teaching research for NCEA L2 and L3 Statistics****What is an Experiment?****The basics of experimental design****Experimentation Glossary****Statistics Education 21st Century NZ****Ethics in Statistics****Experiments at Level 7**

### Classroom Activities

**Fun and Practical Ideas for Level 2 and 3 Experiments: Michael Shadbolt****Using Psychological Tests for the Experiments Standards****Classroom Activities for Teaching the NCEA Level 1 and 2 Statistical Enquiry Standards**

### Tools

# 2.11 Evaluate a statistically based report

This standard is derived from Achievement Objectives S7.3, Evaluate statistically based reports. In particular, identifying sampling and posisble non-sampling errors in surveys, including polls.

Students are required to evaluate a statistically based report using their knowledge of statistical concepts and exercising statistical literacy. Sampling methods, population measures and variables, including polls and surveys, sampling variability, appropriate data displays and sampling and possible non-sampling errors and the effect of sample size need to be studied. Students apply this knowledge to analytically dissect a report from the media within the context and intention of the report. Teachers can use worry questions, writing frames and literacy strategies to encourage students to begin writing. It is an opportunity for students to question what they are presented with from the media, and realise the pitfalls (or motivation) of misinterpreting results.

## Achievement standard and Guides

- Achievement Standard (AS91266) 2015
- Clarification of the standard (AS61266)
- NZQA Exemplars, assessments and reports
- Key Ideas in Statistical Literacy
- Senior Secondary Guide AO S7-3
- Glossary of Statistics terms

## Resources for teaching and learning

### Key Resources

### Teacher Preparation

**Teaching research for NCEA L2 and L3 Statistics****The median outclasses the mean****Developing Statistical Literacy****Statistical Concepts Unpacked****All about election polls****STEW STatistics Education Web - Statistical Literacy resources****STEW, STatistics Education Web****Significant and reliable****Talk back to statistics****How to pass AS 91266****Non-sampling errors**

### Classroom Activities

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

### 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) 2016
- 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 (2012)

## Resources for teaching and learning

### Key Resources

### Teacher Preparation

**Response to the 2014 NZQA external assessments****Risk****Developing Statistical Literacy****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

**Dependent and Independent events KHANAcademy****Probability: risk free****Teaching Risk****Using the Eikosogram to teach conditional and joint probability****Developing Quality in Mathematics Education (DQME)****Analysing Student Attendance Data****Two way table practice****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Legal blood alcohol****Canterbury Mathematics Association 2014 Statistics Teachers Day****Drawing counters from a bag**

### Sourcing Materials

### Curriculum and Assessment

**Canterbury Mathematics Association 2014 Statistics Teachers Day****A response to the first NCEA External Examination: 2.12 by the NZSA**

# 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

**Teaching research for NCEA L2 and L3 Statistics****Hands on activities for teaching risk****Stimulating simulations****A new world of simulations**

### Teacher Preparation

### Classroom Activities

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

### Sourcing Materials

### Curriculum and Assessment

# 3.8 Investigate time series data

## Resources for teaching and learning

### Key Resources

**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]****Videos: Seasonal Decomposition and Forecasting [6 min + 5 min]****Video: Introducing Time Series Data [4:38]****Suggestions for Teaching Time Series****Describing Trends - Statistics New Zealand**

### Teacher Preparation

**Teaching research for NCEA L2 and L3 Statistics****Strategies, tools and prompts to support statistical report writing****iNZight for beginners****Time Series: Managing the practical stuff****Careers in Statistics Posters****Video: Comparing Series [ 4 min]****Videos: Seasonal Decomposition and Forecasting [6 min + 5 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!****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

**NZ Visitor Arrivals (Quarterly)****NZ Visitor Arrivals (Monthly)****NZ Visitor Numbers (Monthly)****NZ Visitor Numbers (Quarterly)****Statistics New Zealand Time Series Datasets****Food Spending****15 Time Series Datasets (2012)****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

**Teaching research for NCEA L2 and L3 Statistics****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: Relationships Between Numeric Variables [5 min]****Video: Trend, scatter and outliers [6:42]****Video: Lines, curves and smoothers [4 min]****Ethics in Statistics****McDonald's food nutritional study****Investigating bivariate measurement data using iNZight**

### Teacher Preparation

**Teaching research for NCEA L2 and L3 Statistics****Strategies, tools and prompts to support statistical report writing****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: Relationships Between Numeric Variables [5 min]****Video: Trend, scatter and outliers [6:42]****Video: Lines, curves and smoothers [4 min]****Ethics in Statistics****Investigating bivariate measurement data using iNZight****Genstat for Yr 11 and 13 Statistical analysis****Regression**

### Classroom Activities

**Data Journalism****Analysing Student Attendance Data****Statistical surprises and stories in bivariate data - Louise Addison****Aiming for Excellence in bivariate data****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****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

**CensusAtSchool 2007 data subset (15,000 rows)****CensusAtSchool 2009 data subset (15,000 rows)****SURF data sets****Data sets for bivariate investigations****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

**Teaching research for NCEA L2 and L3 Statistics****Resources for the "big ideas" behind Statistical reports****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****Using Psychological Tests for the Experiments Standards****Animations for teaching bootstrapping and randomisation****Getting started on VIT modules in iNZight VIT****Ethics in Statistics****Conducting and assessing experiments for 3.11****A guide to the randomisation test****A brief introduction to experimental design**

### Teacher Preparation

**Teaching research for NCEA L2 and L3 Statistics****Resources for the "big ideas" behind Statistical reports****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****Ethics in Statistics**

### Classroom Activities

**Experimental units that are not physical entities****Statistical Experiments MathsNZ****Sampling variation just keeps turning up everywhere!****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****Using Psychological Tests for the Experiments Standards****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

**Teaching research for NCEA L2 and L3 Statistics****Resources for the "big ideas" behind Statistical reports****Margin of Error and testing claims in the media****Margin of Error: Clarifying the rules of Thumb****Hands on activities for teaching risk****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****FAQs for Inferential thinking**

### Teacher Preparation

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

### Classroom Activities

**Margin of Error and testing claims in the media****Hands on activities for teaching risk****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?****Teaching Risk****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****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****The predictive power of polls****Movie issues: Crunching the data**

### Sourcing Materials

**Friends Bully More Than Enemies - Research****International statistical literacy project****Numeracy in the News****Chance news****Health studies****Significance Magazine****FigureNZ****More or Less: Behind the Stats****StatsChat****Bad science****Stats+Stories****OECD data**

### 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

**Having fun with Probability Concepts and Solving Problems****Risk****Hands on activities for teaching 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****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****Analysing Student Attendance Data****Two way table practice****Nine weird tips for adding awesomesauce to Level 2 & 3 Stats!****Statistical surprises and stories - Probability Louise Addison****Some probability teaching ideas****Interactive Probability quiz****Conditional Probability Visualisation****Understanding Probability****Classic problems in Probability****Canterbury Mathematics Association 2014 Statistics Teachers Day****Senior Secondary Guides - Teaching and Learning Activities****Calculating probabilities of independent, combined and conditional events**

### Sourcing Materials

### Curriculum and Assessment

# 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

**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

**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****Canterbury Mathematics Association 2014 Statistics Teachers Day****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

### Curriculum and Assessment

# 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]**