--- title: "Census, sample, experiment or observation" subtitle: "Data and chance · Samples · Lesson 15" --- # Census, sample, experiment or observation **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Every five years Australia asks every household the census questions. A TV ratings company measures viewing in only a few thousand homes. Why doesn't it just measure everyone? :::teacher-note **In one sentence:** Students compare a census and samples on a simulated school, and choose between census, sample, experiment and observation for real questions (AC9M8ST01, node 1). **Students should be able to say:** I can say the difference between a census and a sample. I can tell an experiment from an observation. I can choose a way to collect data and explain why it is practical. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict :::keep-together **A school has 200 students. You ask 20 of them, chosen at random, how long they sleep. Will their mean equal the mean of all 200?** ☐ Exactly the same ☐ Nowhere near ☐ Close, but probably not exactly My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Close, but probably not exactly. A random sample gives an estimate; a census gives the exact value, at much more cost. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Choosing a technique :::keep-together ### Why a sample Here is the routine for choosing. 1. $\text{Question: how much do Year 8s spend on lunch?}$ — Name the population: Year 8 students. 2. $\text{Census? } 180 \text{ students: possible, but slow}$ — Can you measure everyone? At what cost? 3. $\text{Sample of } 40 \text{ chosen at random}$ — Quicker, cheaper, and close if chosen fairly. 4. $\text{Not an experiment: nothing is changed}$ — Measuring as things are: a survey of a sample. **A newspaper wants to know what people in its city think of a new bridge. Why does it survey a sample of 800, not everyone?** ☐ Opinions can't be measured ☐ A sample is more accurate than a census ☐ Asking every person in the city would take too long and cost too much ☐ The law says so ::: :::teacher-note **Answer:** Asking every person in the city would take too long and cost too much When measuring everyone costs too much or takes too long, a fair sample is the sensible choice. ::: :::keep-together ### Find the mistake **Noah plans how to collect data. Click the line where his plan goes wrong.** ``` 1 Noah wants to know how long the batteries from a factory last. 2 A census gives the exact answer, so he decides to test every battery until it runs flat. 3 Then he will know exactly how long the factory's batteries last. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: testing every battery until it is flat leaves the factory nothing to sell. Test a sample instead. ::: :::keep-together ### Experiment **Some students revise with music and some without, chosen at random, then all sit the same test. What technique is this?** ☐ An observation ☐ A census ☐ Not a way to collect data ☐ An experiment: the researcher changes something on purpose ::: :::teacher-note **Answer:** An experiment: the researcher changes something on purpose The music is the thing changed on purpose; the scores show its effect. ::: :::typical ## Matching the technique **Match the technique.** **Bigger samples.** **The census.** **Counting cars.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Techniques :::keep-together ### Small class **A teacher wants the mean height of her class of 25. What is most sensible?** ☐ A sample of 5 ☐ A census: measuring 25 students is quick ☐ An experiment ☐ An observation from across the room ::: :::teacher-note **Answer:** A census: measuring 25 students is quick When the population is small and measuring is easy, a census gives the exact answer. ::: :::keep-together ### Toothpaste **A company wants to know if a new toothpaste reduces cavities. What technique fits?** ☐ Asking the company's staff ☐ An experiment: some use the new toothpaste, some the old, chosen at random ☐ An observation of shop shelves ☐ A census of everyone who brushes their teeth ::: :::teacher-note **Answer:** An experiment: some use the new toothpaste, some the old, chosen at random To see the effect of a change, compare groups given different treatments. ::: :::keep-together ### Testing every bottle **A juice factory checks the sugar in its bottles. A manager says: 'Test every bottle, so we know for sure.' What is wrong with that plan?** ☐ Testing opens the bottle, so there would be nothing left to sell ☐ Nothing: a census is always best ☐ The bottles are too small ☐ Sugar can't be measured ::: :::teacher-note **Answer:** Testing opens the bottle, so there would be nothing left to sell When measuring destroys the item, a sample is the only sensible choice. ::: :::keep-together ### Review: complement **Review: a spinner has equal parts red, blue, green and yellow. What is P(not red)?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3/4 1 − 1/4 = 3/4. ::: ## Make: plan the collection Choose a question about your school or town, such as "How long do students spend on homework?" or "Does a reminder sign reduce littering?" Write the population, the technique you would use, and one reason it suits the question better than the others. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A cereal company wants to check the weight of its boxes. Census or sample? Why?** {{lines-3}} ::: :::teacher-note **Answer:** A sample: weighing every box costs time; checking a random sample of boxes each hour is enough to spot problems. :::