Word (.docx)
Acrobat (.pdf)
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
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
Instructional Items
Instructional Item 1- A teacher wants a representative sample of students at her school to get feedback on this
year’s homecoming theme. Which sample would most likely produce data that is
representative of the population?
- a. She should poll the 30 students in her homeroom class.
- b. She should survey 100 students waiting for the buses after school.
- c. She should randomly sample 50 students from the entire population of the school.
- d. She should talk to each student who eats lunch on campus this upcoming Friday.
Related Courses
Related Access Points
Related Resources
Lesson Plans
Perspectives Video: Experts
Perspectives Video: Professional/Enthusiasts
Problem-Solving Tasks
Text Resources
STEM Lessons - Model Eliciting Activity
Can your school use $5000? What school doesn't?! Well, the money is available, but the student body must decide how the money will be spent!
5K and No More - Producing Data will enable students to fantasize about what they would do to improve their school if allowed to answer the question, "How would $5000 best be spent at your school?" The activity begins with students distinguishing the differences between a sample survey, an experiment, and an observational study through a pre-activity. After this, the students are given five (5) scenarios in which they must discuss the pros and cons of each. In life we want things to be fair, so students must constantly think about bias. The company in this MEA desires the most efficient and effective way to collect information from the students without having to talk to everyone ... who has that kind of time!
Now, just when the students have found the most efficient and effective way to get students to share their thoughts on where the money should go, more information is revealed about the High School. How do we account for the brains and the brawn, the perfect attendee and the most missed days, or for the goth or skater?
Your Savvy Statisticians in the making will figure it out and tell you ALL about it.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
Student Resources
Perspectives Video: Expert
Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.
Download the CPALMS Perspectives video student note taking guide.
Type: Perspectives Video: Expert
Perspectives Video: Professional/Enthusiast
<p>This buzzworthy video features statistics, sampling, and how scientists make inferences about populations.</p>
Type: Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.
Type: Problem-Solving Task
Students are asked to choose the best sampling method for choosing the new School Advisory Panel.
Type: Problem-Solving Task
The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.
Type: Problem-Solving Task
Parent Resources
Perspectives Video: Professional/Enthusiast
<p>This buzzworthy video features statistics, sampling, and how scientists make inferences about populations.</p>
Type: Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.
Type: Problem-Solving Task
Students are asked to choose the best sampling method for choosing the new School Advisory Panel.
Type: Problem-Solving Task
The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.
Type: Problem-Solving Task
