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Generate multiple samples or simulated samples of the same size to measure the variation in estimates or predictions.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Data Analysis and Probability
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Data
- Population (in data analysis)
- Random sampling
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In grade 6, students learned how to calculate the mean and median for numerical data, and they explored how changing values affects the center and variation of numerical data. In grade 7, students experimented with using simulations and comparing the centers and spreads of data. In Mathematics for College Statistics, students combine these middle grades ideas with other benchmarks in this course to examine simulated random samples and naturally occurring sampling variation.- Instruction relates to benchmark MA.912.DP.5.3.
- Instruction includes students randomly sampling from small populations and large populations in order to compare the differences in statistics. With larger populations, it is recommended that students use technology to generate samples.
- Instruction includes using a variety of random sampling techniques, such as simple random, systematic, cluster and stratified sampling to reinforce previous benchmarks.
- In cluster samples, groups should be heterogeneous. In stratified samples, groups should be homogeneous.
- Students should note the variation in statistics from sample to sample and the variation of sample statistics to the population parameters. As well, learners should consider how to reconcile the differences that are seen in population parameters and sample statistics.
- When generating samples, it is important that the sample size is consistent. This allows for a better comparison and relates to the future statistical topic of standard error.
- Instruction includes a discussion on sampling with and without replacement.
Common Misconceptions or Errors
- Students may incorrectly assume that all samples of the same size from the same population will produce the same statistics.
- Students may incorrectly assume that sample statistics will always match population parameters.
- Students may use convenience samples when generating their own data. These convenience samples can lead to biased results.
- Students may confuse cluster sampling and stratified sampling.
Instructional Tasks
Instructional Task 1 (MTR.7.1)- A teacher is interested in the morning commute times of the students in his homeroom class. The teacher finds out that his students drive, walk, ride or bus from home to school each morning. The results of asking all of his homeroom students “How long did it take you to commute from home to school this morning?” is below. The times are all in minutes.
- Consider this homeroom of students as a population. Some parameters are that the mean
morning commute time is 16.5 minutes, 10% of students drive, 13.3% of students walk,
43.4% of students bus to school and 33.3% of students ride to school each day.
- Part A. Use technology to generate a simple random sample of six students from the population above. Record the sample mean and the proportions of students who drive, walk, bus, and ride to school.
- Part B. Use technology to generate another simple random sample six of students from the population above. Record the sample mean and the proportions of students who drive, walk, bus, and ride to school.
- Part C. How do the sample means and proportions from the two samples compare?
- Part D. Use technology to generate a systematic random sample of six students from the population above. Record the sample mean and the proportions of students who drive, walk, bus and ride to school.
- Part E. How do your systematic sample results compare to the results of your first two samples?
- Part F. How do all of your sample statistics compare to the population parameters? Is there any variation?
Instructional Items
Instructional Item 1- All seniors planning to attend college in a graduating class at a smaller Florida high school are surveyed to find out their intended majors. The results are in the table below.
- Part A. Use technology to generate a simple random sample of 12 students from the population above. Record the proportion of business majors.
- Part B. Again, use technology to generate a simple random sample of 12 students from the population above and record the proportion of business majors.
- Part C. How did the proportions of business majors compare from the two samples above? Is there any variation?
Related Courses
This benchmark is part of these courses.
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 - 2024, 2024 and beyond (current))
Related Access Points
Alternate version of this benchmark for students with significant cognitive disabilities.
Related Resources
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Lesson Plans
Perspectives Video: Experts
Problem-Solving Tasks
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