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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

2.9 Making an Inference AS 91264

Inference HOME | Achievement Objectives | Overview | Statistical Cycle
- Write an introduction | Using NZgrapher | Discussing sample statistics
- Box plots | Discussing the boxplot & dotplot | Sampling methods | Sample variability and size
- Informal confidence interval | Comparing two populations - discussion
- Writing a report | Revision

Approximate Lesson Sequence for AS 2.9 Inference

1. Overview & making Box plots, cleaning data, basic descriprion of box plots - skew, groups...
2. Discussing Sample statistics
3. Discussing Sample distribution and features
4. Practice discussing distributions
5. Sampling methods: simple random, systematic, stratified, cluster, census, sampling error
6. Sample variability (n=11 vs 31), The effect of changing sample size on sampling error
7. Writing a Introduction and Research Question
8. Computer practice - input data, write an introduction, make boxplot, discuss sample
9. More practice of introduction & boxplot discussion
10. Finding an Informal confidence intervals
11. Comparing two populations (interpreting an informal confidence interval)
12. Computer practice of making informal confidence interval
13. Applying the PPDAC cycle - Writing a report
14. Practice assessment
15. Practice assessment
16. Feedback
17. Assessment context research
18. Assessment

For Teachers

AS 2.9 Inference AS91264 (4 credit internally assessed)

* Be familiar with the Achievement Standard AS2.9 Inference #91264 (link to NZQA)

* Check the latest information on the NZQA clarifications page as things change all the time, and the exemplars in NZQA may be out of date (as they are in this standard)

* Look over the NZQA Exemplars on AS 2.9 Inference AS2.9 A & AS2.9 B (note these exemplars do not reflect the latest (as of Feb 2013) clarification information

* Material available on the mathstatsfacilitators website AS2.9 Inference page

* AS 2.9 Inference page at CENSUS at schools site

* Check the latest comments on the NZmaths forum (login required)

* Any further ideas / suggestions / resources/ comments / erors. Please email

* AS 2.9 section on Nayland Website updated: June 2014


Useful Links for AS 2.9 Inference (AS 91264)

A list of excellent information and resources and links from CENSUS at schools (AS2.9 page)

Achievement Standard
& Guides

Achievement Standard 2.9 Inference #91264 and exemplars linked to NZQA
Key ideas in Statistical Literacy A brief outline of what needs to be covered at this level
Senior Secondary Guide AO S7-1 Carry out investigations using the statistical enquiry cycle link to TKI
Glossary  of Statistics Terms on TKI


Resources for teaching and learning

Telling Data Stories:  Essential Dialogues for Comparative Reasoning: Pfannkuch, Regan, Wild, Horton, 2010   A research paper with a teachers’ guide to informal comparative reasoning in the Appendix link to (link to
Guidelines to making the call:  Wild, Pfunnkuch, Regan & Horton  The effect of sample size and guidelines for correct interpretation (link to
Animations of Sampling Variation:  Wild, Pfunnkuch, Regan & Horton An active visual representation (link to
Laying the foundations for inference   A video of the Plenary Lecture from 2009 Teachers day, M. Pfannkuch, P. Arnold and M. Regan (link to
The Talk: Building Inferential Reasoning in Statistics, Pfannkuch & Wild A video with handouts and slides (link to
Talk : A Video “Informal Statistical Inference Revisited” C. Wild  with handouts and slides
Teaching Activities:  Linsdsay Smith  Towards Achievement Standard 2.9 from 2011 Statistics Day 
To tag or not to tag  Activity investigating sampling variability for proportions
Kiwi kapers data and activities on the Senior Secondary Guide
In particular: (Link to TKI)

  • Kiwi Kapers 1– uses a simulated data set of Kiwis to explore some of the big ideas:
    • Sampling variation and making inferences
    • Deciding on the sample size  
    • Introduction to stratified sampling
    • PPDAC cycle – using stratified sampling

SURF data set Large synthetic unit-record files on stats nz with activities (link to www.stats.govt.n)
University of Otago video and activity  Property sales (with large data set) (link to

Otago University video series | Maui Dolphin subspecies activity

CMA link to 2.9 Inference resources


Background reading

Enhancing Students’ Inferential  Reasoning:  Arnold, Pfannkuch, Wild,  Regan & Budgett 2011  A research paper about developing students’ inferential reasoning from hands-on to the use of technology, in particular, dynamic animations
Statistical thinking:  Wild and Pfannkuch 1999  A research paper discussing the thought processes involved in statistical problem solving in the broad sense from problem formulation to conclusions
Training teachers in statistical thinking:  Pfannkuch 2008  A research paper that discusses the need for teachers to have a deep knowledge of Statistics to effectively teach students
Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report AMA 2005Pg 61-63, 66-70
Developing statistical literacy 1 Schield: Half truths with statistics
Developing statistical literacy 3 Schield: three types
Developing statistical literacy 4 Schield: competence v citizenship
Textbook:  Jessica Utts Seeing through Statistics, Ch 3.5, 4.2, 4.3, 6,  7




Future Site Development:
AME clarification,
Starter problems,
Progress check 'tests'
Practice worksheets ,
Add in iNZight VIT on sample variation



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