--- marp: true theme: default html: true --- # Census, sample, experiment or observation Data and chance ยท Samples --- ## Today **We are learning to** data can come from everyone (a census), from some (a sample), from an experiment where you change something on purpose, or from watching (an observation). Each has a cost, a time and an accuracy; choose the one that fits the question. - 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. --- ## Why it matters > 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? --- ๐Ÿ’ฌ Discussion ## Predict **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 --- โœ๏ธ Activity ## Try it {{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fdata%2Fcollecting-data%2Fstep-2&code=widget%3A+sample%0Ameasure%3A+sleep%0Amethod%3A+choose%0Aslider+n%3A+5%2C+100%2C+20%2C+5%0A&fresh=1}} [Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/data/collecting-data/?full=step-2#step-2) --- โœ… Check ## What happened? * Close, but probably not exactly. A random sample gives an estimate; a census gives the exact value, at much more cost. --- ๐Ÿ’ฌ Discussion ## Why a sample Here is the routine for choosing. $$\text{Question: how much do Year 8s spend on lunch?}$$ 1) $\text{Census? } 180 \text{ students: possible, but slow}$ โ€” Can you measure everyone? At what cost? 2) $\text{Sample of } 40 \text{ chosen at random}$ โ€” Quicker, cheaper, and close if chosen fairly. 3) $\text{Not an experiment: nothing is changed}$ โ€” Measuring as things are: a survey of a sample. --- โœ… Check ## Why 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 * Answer: Asking every person in the city would take too long and cost too much --- โœ… Check ## 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. ``` * Answer: line 2 --- โœ… Check ## 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 * Answer: An experiment: the researcher changes something on purpose --- โœ๏ธ Activity ## Matching the technique - **Match the technique:** - **Bigger samples:** - **The census:** - **Counting cars:** [Open this step](https://studio.learningwaypoints.com/tutorials/maths/data/collecting-data/?full=step-4#step-4) --- โœ… Check ## 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 * Answer: A census: measuring 25 students is quick --- โœ… Check ## 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 * Answer: An experiment: some use the new toothpaste, some the old, chosen at random --- โœ… Check ## 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 * Answer: Testing opens the bottle, so there would be nothing left to sell --- โœ… Check ## Review: complement **Review: a spinner has equal parts red, blue, green and yellow. What is P(not red)?** * Answer: 3/4 --- โœ๏ธ Activity ## 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. --- โœ… Check ## Exit ticket **A cereal company wants to check the weight of its boxes. Census or sample? Why?** * A sample: weighing every box costs time; checking a random sample of boxes each hour is enough to spot problems.