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AP Statistics

College-level statistics covering data analysis, study design, probability, and inference. Aligned to the College Board AP Statistics Course and Exam Description. Equivalent to an introductory college statistics course.

14 Units

45-60 minutes per unit

What You Will Learn

College Board Aligned

All AP Statistics CED units — from exploring data through inference for categorical and quantitative data.

Real-World Data

Analyze authentic datasets, interpret computer output, and design studies — the way statisticians actually work.

College Credit Potential

A qualifying AP exam score can earn 3-4 college credits (Intro Statistics equivalent) at most universities.

All Units

Exploring Categorical Data

Summarize and display categorical data using frequency tables, bar charts, and pie charts, and draw conclusions from distributions.

•Construct and interpret frequency tables and relative frequency tables for categorical data
•Create and analyze bar charts and pie charts to represent categorical distributions
•Compare distributions of categorical variables across groups using segmented bar charts
+1 more objectives

Displaying Quantitative Data: Distributions

Construct and interpret dotplots, histograms, and stemplots, and describe distributions using shape, center, spread, and unusual features.

•Create dotplots, stemplots, and histograms from quantitative data
•Describe distributions using shape, center, spread, and unusual features (SOCS)
•Identify and interpret symmetric, skewed, and bimodal distributions
+1 more objectives

Describing Quantitative Data with Numbers

Calculate and interpret measures of center and spread including mean, median, standard deviation, IQR, and construct boxplots to summarize quantitative distributions.

•Calculate and interpret mean and median as measures of center
•Calculate and interpret standard deviation and IQR as measures of spread
•Identify and calculate outliers using the 1.5 × IQR rule
+2 more objectives

The Normal Distribution

Use the normal distribution model to calculate probabilities and percentiles using z-scores, the empirical rule, and standard normal tables.

•Describe the properties of the normal distribution and identify the parameters μ and σ
•Apply the empirical rule (68-95-99.7 rule) to estimate probabilities
•Standardize values using z-scores and interpret them in context
+2 more objectives

Exploring Bivariate Data: Correlation and Regression

Analyze relationships between two quantitative variables using scatterplots, correlation, and least-squares regression, including residual analysis.

•Construct and interpret scatterplots, identifying direction, form, strength, and unusual features
•Calculate and interpret the correlation coefficient r
•Find and interpret the equation of the least-squares regression line
+2 more objectives

Collecting Data: Sampling Methods and Study Design

Evaluate sampling methods for bias, distinguish observational studies from experiments, and understand how study design affects the conclusions we can draw.

•Identify and apply probability sampling methods: SRS, stratified, cluster, and systematic sampling
•Recognize sources of bias including voluntary response, convenience sampling, and nonresponse bias
•Distinguish between observational studies and experiments and explain what conclusions each supports
+1 more objectives

Experimental Design

Design experiments using control, randomization, and replication to establish causation, and evaluate the validity of experimental conclusions.

•Identify the components of a well-designed experiment: control group, random assignment, replication
•Explain how randomization controls for confounding variables
•Distinguish between completely randomized designs, block designs, and matched pairs designs
+2 more objectives

Probability: The Foundation of Inference

Apply probability rules, conditional probability, and independence to calculate and interpret probabilities in real-world contexts.

•Interpret probability as long-run relative frequency and apply the basic probability rules
•Calculate probabilities using the addition rule and complement rule
•Determine whether events are independent and calculate conditional probabilities
+2 more objectives

Random Variables and Probability Distributions

Define discrete and continuous random variables, calculate expected value and variance, and apply rules for combining random variables.

•Define a random variable and distinguish between discrete and continuous random variables
•Calculate and interpret the mean (expected value) and standard deviation of a discrete random variable
•Apply rules for combining random variables: sums, differences, and linear transformations
+1 more objectives

Binomial and Geometric Distributions

Calculate and interpret probabilities, means, and standard deviations for binomial and geometric distributions in context.

•Verify the four conditions for a binomial setting and calculate binomial probabilities
•Calculate the mean and standard deviation of a binomial random variable
•Recognize geometric settings and calculate geometric probabilities
+1 more objectives

Sampling Distributions and the Central Limit Theorem

Understand sampling distributions of sample means and proportions, and apply the Central Limit Theorem to describe their behavior.

•Define a sampling distribution and distinguish it from the population distribution and sample data distribution
•Describe the sampling distribution of the sample proportion p̂ including center, spread, and shape
•Describe the sampling distribution of the sample mean x̄ and state the Central Limit Theorem
+2 more objectives

Confidence Intervals for Proportions and Means

Construct and interpret confidence intervals for population proportions and means, and understand the effect of confidence level and sample size on interval width.

•Interpret a confidence interval and confidence level correctly in context
•Construct a one-sample z-interval for a proportion using the four-step procedure
•Construct a one-sample t-interval for a mean and explain when the t-distribution is used
+2 more objectives

Hypothesis Testing: Significance Tests

Conduct and interpret one-sample significance tests for proportions and means, including p-values, significance levels, and Type I and Type II errors.

•State null and alternative hypotheses and explain the logic of significance testing
•Calculate and interpret a p-value in context
•Conduct one-sample z-tests for proportions and t-tests for means using the four-step procedure
+2 more objectives

Inference for Two Samples, Chi-Square, and Regression

Extend inference to two-sample comparisons, chi-square tests for categorical data, and tests for slope in linear regression.

•Conduct two-sample z-tests and confidence intervals for the difference between two proportions
•Conduct two-sample t-tests and confidence intervals for the difference between two means
•Conduct chi-square goodness-of-fit tests and tests for independence or homogeneity
+1 more objectives

AP Statistics. College-level course aligned to College Board CED. Replaces standard Statistics.