--- title: "Statistical investigations" subtitle: "Data and chance · Data · Lesson 9" --- # Statistical investigations **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Do students your age sleep less on school nights? You could argue about it, or you could measure it. What would you need to decide first? :::teacher-note **In one sentence:** Students plan an investigation (question, variable, sample, bias), then summarise and report one in terms of shape, centre and spread (AC9M7ST03, nodes 1 and 2). **Students should be able to say:** I can write a question that data can answer. I can plan a fair sample and name a possible bias. I can report what data show using shape, centre and spread, and say the limits. **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 Think: what would you measure, and from whom? :::keep-together **Which of these can be answered by measuring a number for each student?** ☐ Is sleep important? ☐ How many hours do Year 7 students sleep on school nights? ☐ Should school start later? ☐ Is sleep boring? My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** The first. It names a variable you can measure (hours) and a group (Year 7). The others are opinions or decisions; data can inform them but cannot answer them. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Planning and bias :::keep-together ### Variable type **Hours of sleep is measured on a clock. Is it discrete or continuous?** ☐ Discrete: it is counted ☐ Continuous: any value in a range can occur ☐ Neither ::: :::teacher-note **Answer:** Continuous: any value in a range can occur Measured quantities such as time are continuous. Counted ones, such as the number of pets, are discrete. ::: :::keep-together ### Find the mistake **Kai wants to know how long Year 7 students sleep. Click the line where he draws a conclusion he cannot support.** ``` 1 Kai's question: how many hours do Year 7 students sleep on school nights? 2 He asks the 8 students in his swimming squad. 3 Their median is 8 hours, so Year 7 students sleep 8 hours. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: eight students from one squad are a small group and not a fair sample of Year 7. Swimmers may sleep more or less than others. The result describes his squad. ::: :::keep-together ### A fair sample **Which is the fairest way to choose 20 students from Year 7?** ☐ Ask those who put up their hands ☐ Ask your friends ☐ Pick 20 names at random from the class lists ☐ Ask the first 20 students at the canteen ::: :::teacher-note **Answer:** Pick 20 names at random from the class lists Random selection gives every student the same chance and avoids bias. ::: :::typical ## Compare and report **The best report.** Name both the centre and the spread. **Equal samples.** **Shape.** **An outlier.** **Support or refute.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Investigations :::keep-together ### The mean **Hours of sleep: 7, 8, 9. What is the mean?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 8 (7 + 8 + 9) ÷ 3 = 8 hours. ::: :::keep-together ### Discrete **Which variable is discrete?** ☐ A student's height ☐ The time to run 100 m ☐ The mass of a school bag ☐ The number of siblings a student has ::: :::teacher-note **Answer:** The number of siblings a student has Counted quantities are discrete. The others are measured. ::: :::keep-together ### A biased survey **A survey asks only students who walk to school about how long they sleep. What is the problem?** ☐ The sample is too big ☐ Nothing ☐ Sleep cannot be measured ☐ The sample is biased: walkers may not be like everyone else ::: :::teacher-note **Answer:** The sample is biased: walkers may not be like everyone else A sample must represent the group the question is about. ::: :::keep-together ### Review: median **Review: what is the median of 4, 7, 9, 12, 13?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 9 The middle value of the five is 9. ::: ## Make: your investigation Now write a report of four short parts: the question, the plan (variable, sample and how you would choose it), what the data show (shape, centre, spread), and the limits of your answer. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A survey asks only the first 10 students into school how they travel. Give one reason it may not represent the school.** {{lines-3}} ::: :::teacher-note **Answer:** Students who arrive early may travel differently (for example, by bus or parent drop-off), so the sample is biased. :::