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

Evidence Outcomes 21st Century Skill and Readiness Competencies

Students Can:

  1. 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)
  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)

Inquiry Questions:

  1. How can the results of a statistical investigation be used to support an argument?
  2. What happens to sample-to-sample variability when you increase the sample size?
  3. When should sampling be used? When is sampling better than using a census?
  4. Can the practical significance of a given study matter more than statistical significance? Why is it important to know the difference?
  5. Why is the margin of error in a study important?
  6. How is it known that the results of a study are not simply due to chance?

Relevance & Application:

  1. 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.

Nature Of:

  1. Mathematics involves making conjectures, gathering data, recording results, and making multiple tests.
  2. Mathematicians are skeptical of apparent trends. They use their understanding of randomness to distinguish meaningful trends from random occurrences.
  3. Mathematicians construct viable arguments and critique the reasoning of others. (MP)
  4. Mathematicians model with mathematics. (MP)
  5. Mathematicians attend to precision. (MP)

4 e.g., using simulation. (CCSS: S-IC.2)
For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? (CCSS: S-IC.2)