--- title: "Describing a sample" subtitle: "Data and chance · Samples · Lesson 18" --- # Describing a sample **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A news story says 'Teens sleep 8 hours a night.' Is that every teen, most teens, or a sample's average? A good report says which, and how the sample was chosen. :::teacher-note **In one sentence:** Students take samples of a simulated school, describe each sample's shape, centre and spread, compare two samples, and report an estimate with its method and size (AC9M8ST02, node 2). **Students should be able to say:** I can describe a sample's shape, centre and spread. I can compare two samples by their centres and spreads. I can write a report that gives an estimate for the population and says how the sample was chosen. **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 plot the hours of sleep of 40 students chosen at random. What will the dot plot look like?** ☐ Every dot at the same value ☐ Dots spread evenly from lowest to highest ☐ Most dots in the middle, fewer towards the ends My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Most in the middle, fewer at the ends: most students sleep a similar amount, and a few sleep much more or less. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## From data to report :::keep-together ### Median Here is the routine for a report. 1. $\text{Random sample of } 20 \text{ Year 8s: minutes reading per day}$ — Say the sample: method and size. 2. $\text{Shape: most } 10 \text{ to } 30,\ \text{one outlier at } 120$ — Describe the shape. 3. $\text{Median } 20,\ \text{mean } 25,\ \text{range } 120 - 5 = 115$ — Centre and spread (the outlier pulls the mean up). 4. $\text{Year 8s read about } 20 \text{ minutes a day}$ — An estimate for the population, with its limits. **A sample of 7 students' sleep: 8.0, 9.5, 10.0, 7.5, 9.0, 8.5, 9.0 hours. What is the median, in hours?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 9 In order, the 4th of 7 is 9.0 hours. ::: :::keep-together ### Find the mistake **Leo reports on his sample. Click the line where his report goes wrong.** ``` 1 Leo takes a random sample of 30 students and finds their mean sleep is 8.9 hours. 2 He reports: "The mean sleep of all 200 students is exactly 8.9 hours." 3 He adds that the sample was chosen at random from the school roll. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: a sample's mean estimates the population's; it isn't exactly the same. He should write 'about 8.9 hours, from a random sample of 30'. ::: :::keep-together ### Primary or secondary **A student uses ABS figures on screen time from a national survey. What kind of data is this?** ☐ A census ☐ Secondary data: someone else collected it ☐ Primary data: she is using it ☐ An experiment ::: :::teacher-note **Answer:** Secondary data: someone else collected it Secondary data is collected by others. Say where it came from and how it was collected. ::: :::typical ## Compare and report **Stratified sample.** **Compare two samples.** **Spread.** **The best report.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Describing samples :::keep-together ### Mean **A sample's values are 4, 6, 6, 7, 9, 10, 14. What is the mean?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 8 Total 56 ÷ 7 = 8. ::: :::keep-together ### Shape **A sample's dot plot has most values between 2 and 5, and a long tail of a few values up to 15. How would you describe its shape?** ☐ Symmetric ☐ Evenly spread ☐ Two clusters ☐ Skewed: a long tail to the high side ::: :::teacher-note **Answer:** Skewed: a long tail to the high side A tail stretching to the high values is skewed to the right (positively skewed); the mean is pulled above the median. ::: :::keep-together ### A claim about the school **From a random sample of 50 students, 30 walk to school. What is the best claim about the school?** ☐ Nobody can say anything ☐ Exactly 60% walk ☐ 30 students walk ☐ About 60% of the school's students walk to school ::: :::teacher-note **Answer:** About 60% of the school's students walk to school 30/50 = 60% is an estimate for the school: 'about 60%'. ::: :::keep-together ### Review: systematic **Review: a club has 60 members listed alphabetically. Which gives a systematic sample of 10?** ☐ Every 6th member from a random start ☐ 10 chosen from a hat ☐ The first 10 on the list ☐ 10 from each age group ::: :::teacher-note **Answer:** Every 6th member from a random start 60 ÷ 10 = 6: every 6th from a random start. ::: ## Make: your report Write a short report: the method and size, the shape, the mean, median and range, and what it suggests about how much the school's students sleep. Then compare your estimate with the dashed line. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A random sample of 25 students spends a median of 40 minutes on homework a night (range 0 to 120). Write one sentence about the school.** {{lines-3}} ::: :::teacher-note **Answer:** Students at the school probably spend about 40 minutes on homework a night, though some spend much more, based on a random sample of 25. :::