Statistics
Measures of centre and spread, sampling methods, bias, comparing samples with populations, and planning and running a statistical investigation.
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Statistics is how we find out about a big group without asking everyone. Election polls, TV ratings, fish counts and medical trials all work by studying a sample and using it to say something about a whole population. In this topic you'll revise how to sum up data, learn how to choose a fair sample, spot the bias that can creep into a survey, and see how much you can trust what a sample tells you. You'll finish by running an investigation of your own.
What you'll learn
- 11.01 Measures of centre and spread: a refresher on the mean, median, mode and range, plus the interquartile range, from lists, tables, dot plots, stem-and-leaf plots and histograms.
- Investigation: random sampling. Estimate the mean area of 50 rectangles, and find out why a random sample beats picking "typical" ones yourself.
- 11.02 Sampling methods: census or sample; surveys, observations and experiments; random, systematic, stratified and convenience samples; and using a sample to describe a population.
- 11.03 Bias: leading questions, self-selected and convenience samples, non-response and unfair experiments, and how to design a fair survey.
- 11.04 Compare samples to populations: how sample results vary, why bigger samples give more reliable estimates, and estimating totals and population sizes from samples.
- Investigation: plan and conduct a statistical investigation. Ask a question, collect data fairly and ethically, and report what it tells you about the population, including how sure you can be.
Which level should I pick?
Every worksheet comes in three levels. Each one covers the same skills.
- Level 1 · Warm-up: smaller data sets, simpler numbers and more help along the way. A good place to start.
- Level 2 · Core: the main worksheet for the lesson.
- Level 3 · Challenge: decimals, grouped data, working backwards and problems with more steps and more explaining, for when the Core level feels easy.
Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.
Practice tests
When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.
Curriculum outcomes
What this topic covers in the Australian Curriculum (version 9).
investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques
analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples
compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation
plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty
From earlier years: these lessons revise skills students learnt in earlier years that this year's curriculum builds on, so they aren't linked to an outcome code for this year.
Outcomes lesson by lesson
- 11.01 Measures of centre and spreadFrom earlier years
- Investigation: Random samplingAC9M8ST01
- 11.02 Sampling methodsAC9M8ST01AC9M8ST02
- 11.03 BiasAC9M8ST01
- 11.04 Compare samples to populationsAC9M8ST03
- Investigation: Plan and conduct statistical investigationsAC9M8ST04