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

**Unfolding Secondary TKI activities for teaching L3 Probability Externals - Sun Mee Kim****Working with modern data: A crash course - Anna Fergusson, Liza Bolton****The power of pixels: Modelling with images - Anna Furgusson****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