# Resources for teaching statistics (Last updated 24/04/18)

## Resources for teaching and learning

### Curriculum and Assessment

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.

## Resources for teaching and learning

### Achievement Standard

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

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.

## Resources for teaching and learning

### Curriculum and Assessment

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.

## Resources for teaching and learning

### Sourcing Materials

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.

## Resources for teaching and learning

### Sourcing Materials

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.

## Resources for teaching and learning

### Sourcing Materials

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