Overview

• This in-class activity guides students through the process of selecting a random sample using a biased method and the process of selecting a simple random sample using an unbiased method (random number generator),
• Students will perform both methods of selecting a sample then compare the results.
• The population from which students will sample is an excerpt from a 2001 speech by Justice Sonia Sotomayor^[1], which they were asked to select a “representative” sample of 10 words from the excerpt by eye.
• This activity connects back to Forming Connectons [1C], where students explored data collection and types of variables. It introduces the following vocabulary terms: population, sample, parameter, statistic, unbiased, biased, simple random sample, and sampling frame.
• S2, S4, C2, C4, C6, V1, V4, 01, 03 ← Link to EBTP descriptions 

Prerequisite assumptions

Students should be able to do each of the following after completing the What to Know assignment.

• Identify the population for a given study.
• Identify the parameter of interest for a given study.
• Determine whether a sampling method is biased and explain why.

Intended goals for this activity

After completing this activity, students should understand that collecting a sample “by eye” will, in general, be a biased sampling method. They will also understand that a simple random sample is an unbiased sampling method. They should be able to select a simple random sample from a finite population using a random number generator and explain why a sampling method is unbiased or biased.

Synchronous Delivery and Activity Flow

The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.

Frame the activity (3 minutes)

• Technology
  • Note that students will need access to a web browser to use the Data Analysis Tools, either individually or in  groups. If only the instructor has access to a computer, skip Questions 7–9, demonstrate Question 12 for the class, and then have students answer Questions 10 and 11 using the plot from Question 12 rather than the plot that would have been generated in Question 9.
  • A method for collecting student data and displaying in a dotplot should be set up ahead of time to facilitate Questions 5 and 9. This could be as low-tech as drawing a horizontal axis on a whiteboard and having students place a dot at the location of their sample mean.
• Question 1 — think-pair-share S2, C4, V1, V4, O3
  • Allow 30 seconds for students to think about Question 1 then discuss their answers with a partner for two minutes. Ask some of the pairs to share their ideas.
• Transition to the in-class activity by briefly discussing the Objectives for the activity.

Activity Flow (17 minutes)

• Questions 2-4 — working individually, then moving into groups C6, V1, O1, O3, S2, S4
  • Guiding questions: ““What makes a sample representative of a population?” and “Do you feel your method of sampling led to a representative sample?”
  • After students have answered Questions 2 – 4 individually, have them come together in small groups and come to a consensus of what “representative” means.
• Question 5 — working in groups S4
  • Display a dotplot of student sample means. Students are not introduced to visual displays of quantitative data until In-Class Activity 3.C, but students should be familiar enough with dotplots from previous K–12 work in order for them to understand the plots. To save time as needed, an example appears in the text.
• Question 6 — working in groups S4
  • Students will not yet be familiar with descriptive characteristics like shape, center, spread, and variability. Ask instead about what value they think might represent a “typical” sample and if they can describe the distribution visually.
• Questions 7 – 10 — think-pair-share or small groups C4, V1, O3
  • Have students complete Questions 7 and 8 individually before working in pairs. Assist with the random number generator as needed.
  • In Question 9, collect student data to display a dotplot of the distribution of student-generated sample means. To save time as needed, an example appears in the text.
  • In Question 10, provide the population mean for this excerpt before students continue. The population mean is 4.68.
• Questions 11-13 — small groups C4, V1, O3, O1
  • Throughout these questions, have students compare their answers from their collected data to get a sense of sampling variability.
  • To save time, you may want to either skip Question 12 or do Question 12 on your computer and display for the class using a projector.
  • Students may struggle with the concept that it’s the sampling method that is unbiased/biased, not an individual sample.

Wrap-up/transition (5 minutes)

• Exit tickets can be used to check student understanding at the end of the activity.
  • Have each student write on a piece of paper one key concept they learned from the activity and one concept they have questions about.
• Have students refer back to the Objectives for the activity and check the ones they recognize. Alternatively, they may check the objectives throughout the activity.
• Let students know that the next activity will continue these ideas by discussing sampling methods and sampling bias.
• Assign the homework or Practice and any What to Know pages for the Forming Connections activities you plan to complete in the next class meeting. C2