--- title: "Ways to choose a sample" subtitle: "Data and chance · Samples · Lesson 17" --- # Ways to choose a sample **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** You need 20 students from a school of 200 for a sleep survey, and Year 7s sleep more than Year 10s. How do you pick 20 so the answer is fair? :::teacher-note **In one sentence:** Students take simple random, systematic, stratified and convenience samples of a simulated school, compare them, and choose methods for real situations (AC9M8ST02, node 1). **Students should be able to say:** I can describe simple random, systematic, stratified and convenience sampling. I can work out a systematic step and a stratified share. I can choose a sampling method and say why it is fair. **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 **You pick 20 of the 200 students completely at random. Will you get exactly 5 from each year group?** ☐ Yes, always ☐ Not always: it could be uneven ☐ Never My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Not always. A random sample is fair, but by chance it can have 3 Year 7s and 8 Year 10s. To promise 5 from each, choose 5 at random within each year. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## How each works :::keep-together ### Every kth Here is the routine for a systematic sample. 1. $\text{Population } 120,\ \text{sample } 15$ — Sizes. 2. $k = 120 \div 15 = 8$ — Every 8th. 3. $\text{Random start from 1 to 8: say } 3$ — Start somewhere random. 4. $3, 11, 19, 27, \ldots$ — Add 8 each time until you have 15. **A systematic sample of 40 is taken from a list of 200. Every how many students is chosen?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5 200 ÷ 40 = 5: start at a random student among the first 5, then take every 5th. ::: :::keep-together ### Find the mistake **Ava chooses a sample. Click the line where her method stops being random.** ``` 1 Ava wants a random sample of 20 Year 8 students. 2 She walks around at lunch and picks 20 students she doesn't know, so friendship doesn't affect her choice. 3 That makes it a simple random sample. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: Ava chose the students herself, so who was around at lunch, and whom she noticed, decides the sample. Random means every student has the same chance, such as numbers from a random number generator. ::: :::keep-together ### Why stratify **Year 7s sleep more than Year 10s. Why is a stratified sample (by year) a good choice for a sleep survey?** ☐ It makes the result exact ☐ It only asks Year 7s ☐ It is quicker than random ☐ Each year group gets its fair share, so no year is over- or under-represented ::: :::teacher-note **Answer:** Each year group gets its fair share, so no year is over- or under-represented When groups differ on what you measure, stratifying stops chance from tipping the sample towards one group. ::: :::typical ## Use the methods **Systematic.** **In proportion.** **A patterned list.** **Quota.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Choosing a method :::keep-together ### Names in a hat **Each student's name is put in a hat and 30 are drawn. What method is this?** ☐ Stratified ☐ Systematic ☐ Simple random ☐ Convenience ::: :::teacher-note **Answer:** Simple random Every student has the same chance of being drawn. ::: :::keep-together ### Every 50th **A factory tests every 50th phone off the production line. What method is this?** ☐ Stratified ☐ Convenience ☐ Systematic ☐ Simple random ::: :::teacher-note **Answer:** Systematic A fixed step along a list (or line) is systematic. ::: :::keep-together ### Seniors **A club has 80 junior and 40 senior members. A stratified sample of 15 is taken in proportion. How many seniors?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 5 Seniors are 40 of 120 = 1/3, and 1/3 of 15 = 5. ::: :::keep-together ### Review: bias **Review: a survey of people at a vegan festival asks how often they eat meat. What is the main problem?** ☐ Nothing ☐ The sample is too small ☐ Sampling bias: festival-goers eat less meat than most people ☐ Measurement bias from scales ::: :::teacher-note **Answer:** Sampling bias: festival-goers eat less meat than most people Who was asked pushes the result down. ::: ## Make: pick the best method Then take 10 convenience samples and compare. Write which method you would use for the sleep survey, and why. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A school has 400 Year 9 and 200 Year 10 students. Describe how to take a stratified sample of 30.** {{lines-3}} ::: :::teacher-note **Answer:** In proportion: 20 Year 9s and 10 Year 10s, each chosen at random from its year's list. :::