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

**Developing statistical thinking - Chris Niles****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

**Casting light on probability misconceptions - Stephanie Budgett****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