AP Statistics
Every AP Statistics unit, in order — free video lessons in English and Filipino, a printable worksheet with an answer key for each lesson, and walkthroughs of released free-response questions.
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Exploring One-Variable Data
Displays, center and spread, percentiles, z-scores and the normal distribution.
Unit 1 worksheets
- Categorical vs. Quantitative Variables
- Discrete vs. Continuous Variables
- Dot Plots and Univariate Data
- Analyzing Univariate Data — Dot Plots and Histograms
- Stem-and-Leaf Plots
- Mean vs. Median — Measures of Center
- Percentile Rank from Raw Data
- Percentile Rank — Raw Data and Normal Distributions
- Percentile Rank from Raw Data and Normal Distributions
- Quartiles and Box-and-Whisker Plots
- Summation and Sigma Notation
- Z-Scores and Standard Normal Distribution
- Empirical Rule (68-95-99.7)
- Normal Distribution Probability
- Normal Distribution Sampling Using Z-Table
- Box-and-Whisker Plots, IQR, and Outlier Detection
Exploring Two-Variable Data
Scatterplots, correlation, the least-squares regression line, reading computer output, and transformations.
Unit 2 worksheets
- Explanatory and Response Variables — Scatter Plots
- Correlation and Scatter Plots
- Interpreting Scatter Plots Using FODS
- Least Squares Regression Line
- LSRL from Numerical Summary and Computer Output
- LSRL Predictions
- Linear Transformation on Bivariate Data
- Transforming Data to Achieve Linearity
- Linear Regression & Influential Points
Collecting Data
Populations and samples, random sampling with a random digit table and Table D, bias, and confounding.
Unit 3 worksheets
- Identifying Population and Sample
- Population, Sample, Parameters, and Statistics
- Simple Random Sampling with a Random Digit Table
- Simple Random Sampling with Table D
- Selection Bias, Lurking, and Confounding Variables
- Population, Sample, and Sampling Techniques
- Designing Experiments & Statistical Inference
Probability, Random Variables, and Probability Distributions
Simulation, probability rules, conditional probability, discrete random variables, and the binomial and geometric distributions.
Unit 4 worksheets
- Simulating Experiments with a Random Digit Table
- Probability Introduction — Sample Spaces
- Probability Introduction — Rules and Events
- Classical Probability
- Probability Rules — Events and Operations
- Probability Rules and Models
- Probability — Two-Way Tables and Venn Diagrams
- Probability — Two-Way Tables, Venn Diagrams, and Tree Diagrams
- Conditional Probability
- Conditional Probability Using Tables
- Combinations
- Probability Using Discrete Random Variables
- Mean and Standard Deviation of a Discrete Random Variable
- Binomial Probability
- Mean, Variance & Standard Deviation of a Binomial Distribution
- Geometric Probability Distribution
- Uniform Distribution & Continuous Random Variables
- Discrete and Continuous Random Variables and Normal Distribution
- Simulation Using a Random Number Table
- Conditional Probability
- Conditional Probability — Dependent Events
- Probability & Conditional Probability
- Discrete vs. Continuous Random Variables
- Discrete Random Variables — Probability Distributions
- Random Variables — Probability Distributions
- Mean, Variance, and Standard Deviation of Random Variables
- Geometric Probability Distribution
- Binomial Probability
- Binomial Probability Distribution
- Mean, Variance, and Standard Deviation of Binomial Distributions
Sampling Distributions
How sample proportions and sample means vary, and probabilities from their sampling distributions.
Unit 5 worksheets
- Sampling Distribution: Mean & Standard Deviation
- Sampling Distribution of Sample Proportions
- Sampling Distributions — Mean and Standard Deviation
- Sampling Distributions — Normal Probability
- Normal Distribution Sampling Distribution Probabilities
- Normal Distribution Sampling Distribution Probabilities (TI-84)
- Normal Distribution Sampling Distribution Probability
Inference for Categorical Data: Proportions
Confidence intervals and significance tests for one and two proportions, and Type I and Type II errors.
Unit 6 worksheets
- Confidence Interval for Population Proportion
- Confidence Intervals for Population Proportion
- Hypothesis Testing: Null & Alternative Hypotheses
- Hypothesis Testing for One Sample Proportion
- Hypothesis Testing for Two-Sample Proportions
- Type I and Type II Errors
- Hypothesis Testing: Two-Proportion Z-Test
- Confidence Interval for Population Proportion
- Confidence Intervals for Population Proportions
- Hypothesis Testing — Null and Alternative Hypotheses
- Hypothesis Testing for One-Sample Proportion
- Hypothesis Testing for Two-Sample Proportions
- Type I and Type II Errors in Hypothesis Testing
Inference for Quantitative Data: Means
Confidence intervals and t-tests for one mean, two means and matched pairs, plus choosing a sample size.
Unit 7 worksheets
- Confidence Intervals: Estimating the Population Mean
- Confidence Intervals for Population Mean
- Confidence Intervals (t-Distribution)
- Confidence Intervals for the Population Mean
- Determining Minimum Sample Size for Estimating a Population Mean
- Confidence Intervals Using the Paired t-Design
- Hypothesis Testing for Population Mean
- Hypothesis Testing for Two Sample Means
- Matched Pairs Design & Paired t-Test
- Confidence Intervals — Estimating Population Mean
- Confidence Intervals — Population Mean (t-Distribution)
- Confidence Intervals Using t-Distribution
- Confidence Intervals Using Paired t-Design
- Determining Sample Size for Estimating Population Mean
- Hypothesis Testing for Population Mean
- Hypothesis Testing for Two-Sample Means
- Matched Pairs Design — Paired t-Test
Inference for Categorical Data: Chi-Square
Chi-square tests for goodness of fit, independence and homogeneity.
Inference for Quantitative Data: Slopes
Confidence intervals and significance tests for the slope of a regression line. Dedicated Unit 9 lessons aren't published yet. The core skill is reading regression computer output, so start with LSRL from Computer Output and its worksheet below.
Unit 9 worksheets
AP Exam Free-Response Walkthroughs
Dr. E works through free-response questions from released AP Statistics exams, step by step. The official questions and scoring guidelines are on AP Central; each walkthrough comes with a Numberbender practice worksheet on the same idea.
Where Numberbender started: an AP Statistics classroom
Dr. Peter Esperanza began teaching AP Statistics at Barstow High School in 2009. In 2012 he flipped the class — short video lessons the night before, problems together in class the next day — and those videos became Numberbender.
The year before the flip, exactly one of his students passed the AP exam. Once the class was flipped, about ten students a year were passing, with scores of 3, 4 and 5. The lessons on this page come from that classroom.