AP Statistics Study Guide

Key Exam Details

• Equivalent to a first-semester, college-level statistics course.
• Exam is 3 hours, includes 46 questions: 40 multiple-choice (50% of exam) and 6 free-response (50% of exam).
• Content categories:
  • Exploring One-Variable Data: 15-23%
  • Exploring Two-Variable Data: 5-7%
  • Collecting Data: 12-15%
  • Probability, Random Variables, and Probability Distributions: 10-20%
  • Sampling Distributions: 7-12%
  • Inference for Categorical Data (Proportions and Chi-Square): 12-15%, 2-5%
  • Inference for Quantitative Data (Means and Slopes): 10-18%, 2-5%

Exploring One-Variable Data

• Variables and Frequency Tables:
  • Categorical vs Quantitative variables.
  • Quantitative variables can be discrete or continuous.
  • Frequency and relative frequency tables.
• Graphs for Categorical Variables:
  • Bar charts for displaying frequencies or relative frequencies.
• Graphs for Quantitative Variables:
  • Histograms for displaying intervals of data.
  • Stem-and-leaf plots.
  • Dot plots.
• Distribution of Quantitative Data:
  • Described using shape, center, variability, and unusual features.
  • Concepts of skewness, modality, outliers, gaps, and clusters.

Summary Statistics and Outliers

• Measures of center: mean, median, quartiles, percentiles.
• Measures of variability: variance, standard deviation, range, IQR.
• Outliers:
  • 1.5IQR rule for outliers.
  • Resistance of statistics: median/IQR (resistant) vs mean/SD/range (non-resistant).
• Graphs of Summary Statistics:
  • Boxplots representing the five-number summary.

The Normal Distribution

• Characterized by mean and standard deviation.
• Empirical Rule:
  • 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD.
• Z-score: Standardized score indicating how far a value is from the mean.

Exploring Two-Variable Data

• Two Categorical Variables:
  • Use of contingency tables.
• Two Quantitative Variables:
  • Scatterplots, association (positive/negative), linearity.
  • Correlation measures the strength and direction of a linear relationship.
  • Linear Regression: Predict y from x using the equation y = a + bx.
  • Residuals: Difference between observed and predicted values.
  • Coefficient of Determination (R²): Proportion of variance in y explained by x.

Collecting Data

• Sampling Methods:
  • Simple random sampling, stratified sampling, cluster sampling, systematic sampling.
• Problems with Sampling:
  • Bias: Voluntary response, undercoverage, nonresponse, question wording.
• Experimental Design:
  • Control vs treatment groups, randomization, blinding, placebo effect.

Probability and Distributions

• Basic Probability: Calculation and interpretation.
• Joint and Conditional Probability: Understanding dependencies between events.
• Random Variables: Discrete vs Continuous.
• Binomial and Geometric Distributions:
  • Bernoulli trials and their distributions.

Sampling Distributions

• Central Limit Theorem: Distribution of sample means is approximately normal.
• Sampling Distribution for Proportions and Means:
  • Conditions and calculations for proportions and means.

Inference for Categorical Data: Proportions

• Confidence Intervals: Estimating population parameters using sample data.
• Hypothesis Testing:
  • Null and alternative hypotheses.
  • Errors: Type I (false positive) and Type II (false negative).

Inference for Quantitative Data: Means

• Use of t-distribution when population standard deviation is unknown.
• Confidence Intervals and Hypothesis Tests:
  • Steps for constructing intervals and performing tests.

Inference for Categorical Data: Chi-Square

• Tests: Goodness-of-fit, homogeneity, and independence.
• Expected Counts: Comparison of observed vs expected frequencies.

Inference for Quantitative Data: Slopes

• Linear Model: Testing the relationship between variables using slopes.
• Confidence Intervals and Hypothesis Tests for slopes.

Tips and Suggested Readings

• Various tips provided for free response questions and understanding statistical concepts.
• Recommended textbooks for deeper understanding.

This study guide provides a comprehensive overview of the topics and skills necessary for the AP Statistics exam, including practical examples and common statistical methods used in analyzing data.