The visual guide to
AP® Statistics
5 units, 131 topics. Each topic is explained in writing, drawn as a lesson you can watch, and checked with practice questions.
/
Each unit is as wide as its share of the exam's multiple-choice section.Filled: topics you've opened.
Unit 1Exploring One-Variable Data and Collecting Data
- Populations, Samples, and Statistical Studies
- Asking a Statistical Question
- Observational Units, Variables, Parameters, and Statistics
- Categorical, Discrete, and Continuous Variables
- Frequency and Relative Frequency Tables
- Bar Charts and Pie Charts
- Comparing Categorical Displays
- Dotplots and Stemplots
- Histograms and Bin Width
- Cumulative Relative Frequency Graphs
- Shape: Symmetry, Skew, and Modes
- Gaps, Clusters, and Unusual Features
- Mean, Median, and Which One to Trust
- Quartiles, Percentiles, and the Five-Number Summary
- Range, IQR, and Standard Deviation
- Outliers and the 1.5 IQR Rule
- Changing Units and Linear Transformations
- Boxplots and What They Hide
- Reading Shape from the Mean and the Median
- Comparing Two Distributions Side by Side
- z-Scores and Relative Position
- Comparing z-Scores Across Different Distributions
- Census, Survey, Experiment, and Observational Study
- Why an Observational Study Cannot Show Cause
- Generalizing from a Sample
- Simple Random Samples
- Stratified and Cluster Sampling
- Systematic Sampling and Choosing a Method
- Undercoverage, Nonresponse, and Voluntary Response
- Response Bias and Question Wording
- Control, Randomization, and Replication
- Placebos, Blinding, and Confounding
- Completely Randomized, Blocked, and Matched Pairs Designs
- What an Experiment Lets You Conclude
Unit 2Probability, Random Variables, and Probability Distributions
- Two-Way Tables
- Segmented Bar Charts for Two Categorical Variables
- Joint, Marginal, and Conditional Relative Frequencies
- Association in Two-Way Tables
- Designing a Simulation
- The Law of Large Numbers
- Probability of an Event and Its Complement
- Venn Diagrams and the Sample Space
- Mutually Exclusive Events
- Conditional Probability
- Tree Diagrams and the Multiplication Rule
- Independent Events
- The General Addition Rule
- Choosing Among the Probability Rules
- Discrete Random Variables and Their Distributions
- Continuous Random Variables and Density Curves
- Mean of a Random Variable
- Standard Deviation of a Random Variable
- What Makes a Binomial Setting
- Binomial Probabilities
- Mean and Standard Deviation of a Binomial
- The Normal Curve and the Empirical Rule
- Normal Probabilities and Standardizing
- Working Backward from an Area
- Checking Whether a Distribution Is Normal
- What a Sampling Distribution Is
- The Central Limit Theorem
- Bias and Variability of a Statistic
- Combining Random Variables
- The Geometric Distribution
Unit 3Inference for Categorical Data: Proportions
- Unbiased Estimators
- Point Estimates and Their Variability
- The Sampling Distribution of p-hat
- Conditions for the Normal Approximation
- What a Confidence Interval Is
- Building a One-Proportion z-Interval
- Margin of Error and Sample Size
- Interpreting a Confidence Interval
- Using an Interval to Judge a Claim
- Confidence Level, Width, and Sample Size
- Hypotheses for a Population Proportion
- Conditions for a Proportion Test
- What a p-Value Actually Measures
- One-Sided and Two-Sided p-Values
- Significance Level and the Decision
- Carrying Out a One-Proportion z-Test
- Stating a Conclusion in Context
- Type I and Type II Errors
- Power of a Test
- Trading Off the Two Errors
- Sampling Distribution for a Difference of Proportions
- Confidence Interval for a Difference of Proportions
- Reading an Interval That Contains Zero
- Justifying a Claim About Two Proportions
- Setting Up a Two-Proportion Test
- Carrying Out a Two-Proportion z-Test
- Concluding About Two Proportions
- The Chi-Square Distribution
- Choosing Homogeneity or Independence
- Expected Counts and the Chi-Square Statistic
- Chi-Square p-Values and Conclusions
- Chi-Square Goodness-of-Fit
Unit 4Inference for Quantitative Data: Means
- The Sampling Distribution of x-bar
- Conditions for Inference About a Mean
- The t-Distribution
- Building a One-Sample t-Interval
- Paired Data and Mean Differences
- Interpreting an Interval for a Mean
- Judging a Claim with a Mean Interval
- Hypotheses for a Population Mean
- Conditions for a One-Sample t-Test
- Carrying Out a One-Sample t-Test
- Concluding a Mean Test
- Sampling Distribution for a Difference of Means
- Two-Sample t-Interval for a Difference of Means
- Degrees of Freedom and the Conservative Rule
- Justifying a Claim About Two Means
- Setting Up a Two-Sample Mean Test
- Carrying Out a Two-Sample t-Test
- Choosing the Right Mean Procedure
Unit 5Regression Analysis
- Scatterplots
- Describing a Scatterplot
- Outliers and Influential Points
- What Correlation Measures
- Interpreting r
- Correlation, Causation, and Lurking Variables
- Reading a Regression Equation
- Extrapolation and Prediction
- Residuals
- Residual Plots
- Interpreting Residuals in Context
- Where the Least-Squares Line Comes From
- Slope, Intercept, and the Point of Means
- r-Squared and the Spread of the Residuals
- Departures from Linearity and Transformations
- The Sampling Distribution of the Slope
- Inference for the Slope of a Regression Line