New Colorado P-12 Academic Standards
Current Display Filter: Mathematics - All - by Specific Prepared Graduate Competency - (Remove PGC Filter)
Content Area: Mathematics
Grade Level Expectations: High School
Standard: 3. Data Analysis, Statistics, and Probability
Prepared Graduates: (Click on a Prepared Graduate Competency to View Articulated Expectations) - (Remove PGC Filter)
Concepts and skills students master:
2. Statistical methods take variability into account supporting informed decisions making through quantitative studies designed to answer specific questions
||21st Century Skill and Readiness Competencies|
- Understand and evaluate random processes underlying statistical experiments. (CCSS: S-IC)
- Describe statistics as a process for making inferences about population parameters based on a random sample from that population. (CCSS: S-IC.1)
- Decide if a specified model is consistent with results from a given data-generating process.4 (CCSS: S-IC.2)
- Make inferences and justify conclusions from sample surveys, experiments, and observational studies. (CCSS: S-IC)
- Identify the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. (CCSS: S-IC.3)
- Use data from a sample survey to estimate a population mean or proportion. (CCSS: S-IC.4)
- Develop a margin of error through the use of simulation models for random sampling. (CCSS: S-IC.4)
- Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. (CCSS: S-IC.5)
- Define and explain the meaning of significance, both statistical (using p-values) and practical (using effect size).
- Evaluate reports based on data. (CCSS: S-IC.6)
- How can the results of a statistical investigation be used to support an argument?
- What happens to sample-to-sample variability when you increase the sample size?
- When should sampling be used? When is sampling better than using a census?
- Can the practical significance of a given study matter more than statistical significance? Why is it important to know the difference?
- Why is the margin of error in a study important?
- How is it known that the results of a study are not simply due to chance?
Relevance & Application:
- Inference and prediction skills enable informed decision-making based on data such as whether to stop using a product based on safety concerns, or whether a political poll is pointing to a trend.
- Mathematics involves making conjectures, gathering data, recording results, and making multiple tests.
- Mathematicians are skeptical of apparent trends. They use their understanding of randomness to distinguish meaningful trends from random occurrences.
- Mathematicians construct viable arguments and critique the reasoning of others. (MP)
- Mathematicians model with mathematics. (MP)
- Mathematicians attend to precision. (MP)