This unit starts before any graph: with the question of who is in the data. You will see why a sample differs from the population it comes from, take samples by chance, by a rule and by group, and meet the ways a survey can lean.
Then the unit returns to the scatter graph and the line of best fit with a harder question: how far can a prediction be trusted? The last lesson puts the pieces in one chain, from a question and a sampling plan to a conclusion you can defend.
A graphic display calculator (GDC) is optional all the way through. Lessons 2 and 5 have a closed “With a GDC” section to open if you have one; everything else is done by hand.
The lessons, in order
- Lesson 1 · Population and sample Population, sample and the sample mean as an estimate, estimating a total from a sample share, capture and recapture, and why samples from one population differ. Grow a sample one handful at a time and watch its mean settle, then compare four samples of the same size. No calculator
- Lesson 2 · Random and systematic sampling The sampling frame, a simple random sample from random numbers (skipping repeats and numbers outside the list), a systematic sample from an interval and a start, and the danger of a repeating pattern. Move the interval and the start of a systematic sample over a repeating production line, then see how the interval comes from the sample size. GDC optional
- Lesson 3 · Stratified and quota sampling Strata and proportional allocation, sizing a stratified sample, estimating a population mean from strata, and quota sampling and why it is not random. Resize a stratified sample group by group, then move the share of one group in a survey and watch the estimate leave the truth. No calculator
- Lesson 4 · Bias in surveys Sampling bias, self-selection, non-response, wording bias, the response rate and the range of what non-responders could change, and the difference between bias and random wobble. Remove replies from one group to see the estimate drift, then grow a sample from 25 to 1600 and see which error shrinks. Scientific calculator
- Lesson 5 · Interpolation and extrapolation Predicting from the equation of a line of best fit, interpolation and extrapolation, the effect of scatter on a prediction, and judging a claim made far outside the data. Slide a prediction along a seedling's line and reveal later measurements, then compare tight and loose dots about the same line. GDC optional
- Lesson 6 · Planning an investigation Planning a two-variable investigation, building a line of best fit from the mean points of the lower and upper halves, predicting within the data, and judging a conclusion against its sampling and its range. Compare lines built from two different samples, then build one line by hand in four stages. No calculator
Every lesson has a teacher page with the answers, the misconceptions each wrong answer reveals, discussion questions, differentiation and support for students learning in English, and extra questions in three tiers.