Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

• Data 
• Population (in data analysis) 
• Random sampling 
• Statistical question

Vertical Alignment

Previous Benchmarks

• MA.6.DP.1.1 
• MA.7.DP.1.3

Next Benchmarks

Purpose and Instructional Strategies

In grades 6 and 7, students examined formulating statistical questions to formulate data and used proportional relationships to make predictions about a population. In Mathematics for College Statistics, students explore how they can extend this idea to random sampling in order to produce data that is representative of the population. 

• Instruction references MA.912.DP.5.1 to reinforce that often times a population is too large to collect data from each individual; a sample is selected as a subset of the population. In order to produce a sample that has similar demographics to the population, a random sample should be selected. 
• Instruction explains how convenience samples and voluntary response samples lead to biased samples that most likely do not represent the entire population. 
  • For example, if a college professor talks to the first 50 students entering the on campus library on a Monday morning, this would be a biased convenience sample that would not share the characteristics of all students in the population. Students who only take evening classes or who only take online classes are most likely not represented by this sample. 
• Students should understand that by randomly selecting a sample from the entire population everyone/everything in the population has an equal chance of being selected. This lack of bias allows for a variety of people/objects to be selected so that various characteristics are present in the sample. Therefore, the makeup of the sample is similar to that of the population, and we can say the sample is representative. 
• Instruction includes using technology and/or applets to randomly select a sample from a population to see how the sample has similar characteristics when compared to the population. 
• Avoid measurement bias by having an appropriate statistical question. When asking a question to collect data that is representative of the population, the question should be clear, concise and free of any language that may bias the response of any participants.

Common Misconceptions or Errors

• Students may have initially misconceptions regarding how a random sample does not lead to a biased sample. They may incorrectly assume that randomly selecting from the population will inadvertently leave out certain groups. Using simulations and applets can help with this misconception.

Instructional Tasks

Instructional Task 1 (MTR.4.1, MTR.7.1) 

• A manager for an office supply store has a large shipment of 2,000 calculators being delivered today. If more than 2% of the calculators are defective, he will not accept the shipment and will have to send them all back. Due to time constraints he cannot test all 2,000 calculators to make sure enough of them work; he can only test 100. The manager decides that he will take a sample of 100 calculators and test them to estimate the percentage in the shipment that are defective. 
  • Part A. Why would checking the first 100 calculators most likely not produce data that is representative of the population? Explain. 
  • Part B. What would be the best way to get sample that produces data that is representative of the population? Elaborate on how the manager could get this type of sample. 
  • Part C. Suppose the manager takes a sample using the method that you wrote about in Part B, and he finds that 6 out of 100 calculators are defective and do not work. What should the manager do? Can he feel confident even though he has only sampled 100 calculators? Explain your reasoning

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.