Collect and display data, find its centre and spread, and compare data sets; then list what can happen, give it a probability, and test it with experiments.
Each lesson works two ways. Students can work through the online tutorial at their own pace (it checks their answers and saves their progress in their browser), or you can teach it to the whole class from the slides, then send students into the tutorial for the Modify and Make steps.
Every lesson guide has plain-language notes, the answers to every check, a solution for every task, and slides and a worksheet for Waypoints Prepare. These guide pages are not linked from student pages, but they are not secret either: keep printed Teacher editions for answers you do not want students to find.
Whole-course cheat sheet: Open to print (every command, grouped by unit: a handout for the final challenge)
Counting and measuring, mean, median, mode and range, stem-and-leaf plots, and comparing two data sets.
Numerical data is discrete when it is counted (siblings, goals) and continuous when it is measured (height, time), and measured values are always rounded. A data set is summed up by its centre (mean: total ÷ count; median: the middle value once sorted; mode: the most common) and its spread (range: highest − lowest).
Which centre is most useful depends on the data: an outlier drags the mean, so the median usually describes a typical value better; with no outliers the mean uses every value; for "most common" use the mode. A stem-and-leaf plot keeps every value and shows the shape (symmetrical or skewed, clusters, gaps, outliers). To compare two data sets, compare centre and spread, with numbers and in context.
Statistics in the news, in sport and in science all rest on choosing a fair summary and comparing fairly. Year 8 builds sampling and variation on these ideas.
The lesson Statistical investigations gives the shape of one (question, plan, sample and bias, display, summary, report), with sleep as the example. The investigation itself is best done in class too, using the tools from these lessons: pose a question about the class (for example, "Do we sleep less on school nights?"), plan what to measure and how, collect the data, display it (dot plot or stem-and-leaf), find the centre and spread, compare groups, and report a conclusion with its limits (who was asked, how many, how it was measured).
discrete, continuous, mean, median, mode, range, outlier, stem-and-leaf plot, key, symmetrical, skewed, distribution.
Cheat sheet: Open to print (A4, with board pictures) · Markdown
Sample spaces and probabilities, then experiments: what happens in 10 trials, and in 1000. Year 8: complements, Venn diagrams, two-way tables, grids and trees, and, or, not, and simulations.
The sample space lists every possible outcome. When outcomes are equally likely, ; when they are not (a spinner with a bigger sector, a bag with more of one colour), use the sizes or counts. Probabilities run from 0 (impossible) to 1 (certain) and all the outcomes' probabilities add to 1.
A probability predicts: expected count = probability × trials. An experiment gives a relative frequency (count ÷ trials), which varies a lot over a few trials and settles close to the probability over many (the law of large numbers).
Large experiments and simulations are how probabilities are estimated when no sample space of equal outcomes exists: a drawing pin landing point-up, a medicine working, a machine failing.
An event and its complement (not A) cover every outcome once, so P(not A) = 1 − P(A); "at least one" is quickest as 1 − P(none). Two events that just can't happen together are not complementary unless they also cover everything. Two events one after the other make pairs, listed once each in a grid or a tree diagram (HT and TH are different outcomes); count by multiplying. Two properties of one group make four groups (one, the other, both, neither), shown by a Venn diagram or a two-way table: write "both" first. And is the overlap; or is one, the other or both, so P(A or B) = P(A) + P(B) − P(A and B). A simulation runs many trials quickly; its relative frequency estimates the probability, and a short run can be well off. The common slips: counting the overlap twice, merging HT and TH, and trusting 20 trials.
outcome, sample space, event, probability, equally likely, expected count, relative frequency, trial, law of large numbers, complement, two-way table, Venn diagram, tree diagram, compound event, simulation.
Cheat sheet: Open to print (A4, with board pictures) · Markdown
Year 8: census, sample, experiment and observation; bias; ways to choose a sample; describing a sample; how samples vary; and investigations that infer about a population.
The population is everyone a question is about. A census measures all of them: exact, but slow, costly, and sometimes impossible (testing every battery leaves none to sell). A sample measures some, and gives an estimate. An experiment changes something on purpose and measures the effect; an observation watches without changing anything.
Bias pushes a result one way: sampling bias (who is asked: people at a gym, phone-in callers), response bias (how they are asked: leading questions, no privacy) and measurement bias (a faulty tool). A bigger sample doesn't fix bias.
Fair ways to choose: simple random (every member the same chance), systematic (every kth from a random start, k = population ÷ sample size) and stratified (at random within each group, in proportion). Convenience and quota samples let a person choose, so they can be biased.
Fair samples still differ by chance: sampling variation. Their results scatter around the population's value, and bigger samples vary less. So an inference about the population says "about", names the sample's size and method, stays within the population sampled, and is collected ethically (consent, anonymity, neutral questions).
Polls, medical trials, product testing, the ABS: almost every number in the news comes from a sample. Knowing how it was chosen and how big it was is how to judge it.
population, census, sample, experiment, observation, bias, simple random, systematic, stratified, convenience, quota, primary and secondary data, distribution, sampling variation, inference, uncertainty.
Cheat sheet: Open to print (A4, with board pictures) · Markdown