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AP Statistics

Audience

This course is designed for high-school students who are preparing for the AP Statistics examination and who wish to earn college credit or advanced placement for an introductory, non-calculus-based statistics course.
It is appropriate for students interested in mathematics, science, social science, business, health sciences, engineering, data science, and any field where data-driven reasoning is essential.

The course emphasizes statistical thinking, data analysis, and interpretation, rather than algebraic manipulation or formal proofs.

Prerequisites

Students should have successfully completed:

  • A full sequence of high-school algebra (Algebra I and II)
  • Experience with linear functions, systems of equations, and basic function interpretation
  • Comfort with graphing and numerical reasoning

Calculus is not required and is not used in this course.

Overview

AP Statistics introduces students to the major concepts and tools used for collecting, analyzing, and drawing conclusions from data. The course follows the framework defined by the :contentReference[oaicite:0]{index=0} and is designed to be equivalent to a one-semester, introductory college statistics course.

Students learn to explore data, design studies, understand probability, model randomness, and perform statistical inference. A strong emphasis is placed on real-world data, conceptual understanding, communication of results, and statistical reasoning rather than formula memorization.

Throughout the course, students are expected to justify conclusions, assess assumptions, interpret results in context, and recognize the limitations of statistical methods.

Units of Study

  1. Exploring One-Variable Data
  2. Graphical and numerical summaries of distributions
  3. Shape, center, spread, and outliers

  4. Normal distributions and standardization

  5. Exploring Two-Variable Data

  6. Categorical vs. categorical data
  7. Scatterplots and correlation

  8. Linear regression and residual analysis

  9. Collecting Data

  10. Sampling methods and bias
  11. Observational studies vs. experiments

  12. Random assignment and causation

  13. Probability, Random Variables, and Distributions

  14. Simulation of random events
  15. Probability rules
  16. Discrete random variables and expected value

  17. Binomial and geometric distributions

  18. Sampling Distributions

  19. Sampling variability
  20. Sampling distributions of proportions and means

  21. Central Limit Theorem

  22. Inference for Categorical Data: Proportions

  23. Confidence intervals for proportions
  24. Hypothesis tests for one and two proportions

  25. Type I and Type II errors

  26. Inference for Quantitative Data: Means

  27. Confidence intervals for means
  28. One-sample and two-sample t-tests

  29. Paired data analysis

  30. Inference for Categorical Data: Chi-Square

  31. Goodness-of-fit tests

  32. Tests for homogeneity and independence

  33. Inference for Quantitative Data: Slopes

  34. Confidence intervals and hypothesis tests for regression slopes
  35. Interpreting linear relationships in context

Concepts Covered

  • Data visualization and descriptive statistics
  • Measures of center and variability
  • Linear relationships and regression modeling
  • Study design and data collection methods
  • Probability rules and simulation
  • Random variables and probability distributions
  • Sampling distributions and the Central Limit Theorem
  • Statistical inference:
  • Confidence intervals
  • Hypothesis testing
  • p-values and significance
  • Interpretation of statistical results in real-world contexts
  • Communication of statistical conclusions using proper notation and language

Concepts NOT Covered

The following topics are intentionally excluded from AP Statistics:

  • Calculus-based probability or inference
  • Multivariable calculus or optimization
  • Bayesian inference
  • Time series analysis
  • Multivariate regression
  • Nonparametric inference methods
  • Advanced probability theory (e.g., continuous distributions beyond the normal)
  • Machine learning or predictive modeling
  • Statistical proofs and theoretical derivations

Learning Objectives Sorted by the Six Levels of the 2001 Bloom Taxonomy

Remember

  • Recall definitions of key statistical terms
  • Identify types of variables and data
  • Recognize common statistical symbols and notation
  • Recall formulas for basic statistics and probability rules

Understand

  • Explain the meaning of center, spread, and shape of distributions
  • Interpret graphical displays of data
  • Describe the purpose of sampling and randomization
  • Explain what confidence intervals and p-values represent

Apply

  • Construct and interpret graphs and numerical summaries
  • Calculate probabilities using rules and simulations
  • Perform confidence interval calculations
  • Conduct hypothesis tests using appropriate procedures
  • Use technology to analyze data sets

Analyze

  • Compare distributions using graphical and numerical methods
  • Distinguish between correlation and causation
  • Evaluate the design of studies for bias and validity
  • Analyze residual plots to assess model fit
  • Determine whether assumptions for inference are satisfied

Evaluate

  • Assess the appropriateness of statistical methods
  • Critique conclusions drawn from data analyses
  • Judge the strength of evidence provided by statistical tests
  • Evaluate the limitations of statistical studies
  • Interpret results in context and assess practical significance

Create

  • Design sampling plans and experiments
  • Develop statistical arguments supported by data
  • Write clear, well-structured statistical reports
  • Communicate findings using appropriate graphs, language, and notation
  • Propose improvements to data collection or analysis methods