AP Statistics AP统计学
📌 Course at a glance
· 9 units · key topics drilled across the official outline
· Next exam: 2026-05-13 · 2026-05-13
📝 Full chapter-by-chapter lecture walkthroughs are being written. This page is the course outline — every unit and topic that will be covered, with key concepts you can already start to recognise. Use it as a study map; the chapter notes drop in over the coming weeks.
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Course outline
Unit 1 · Exploring One-Variable Data 探索单变量数据
Exam weight: 15-23%
1.1 — Introducing Statistics: What Can We Learn from Data? 统计学入门：我们能从数据中学到什么？
· Types and sources of data · Fundamental questions of statistics · Individuals and variables
1.2 — The Language of Variation: Variables 变异的语言：变量
· Categorical variables · Quantitative variables · Classification of variables
1.3 — Representing a Categorical Variable with Tables 用表格表示分类变量
· Frequency tables · Relative frequency tables · Frequency and proportion
1.4 — Representing a Categorical Variable with Graphs 用图形表示分类变量
· Bar charts · Pie charts · Graphical display of categorical data
1.5 — Representing a Quantitative Variable with Graphs 用图形表示定量变量
· Histograms · Stem-and-leaf plots · Dotplots
1.6 — Describing the Distribution of a Quantitative Variable 描述定量变量的分布
· Shape · Center · Spread · Outliers · Skewness
1.7 — Summary Statistics for a Quantitative Variable 定量变量的汇总统计量
· Mean · Median · Standard deviation · Interquartile range · Range
1.8 — Graphical Representations of Summary Statistics 汇总统计量的图形表示
· Boxplots · Five-number summary · Modified boxplots
1.9 — Comparing Distributions of a Quantitative Variable 比较定量变量的分布
· Side-by-side boxplots · Back-to-back stem-and-leaf plots · Language for comparing distributions
1.10 — The Normal Distribution 正态分布
· Normal curve · 68-95-99.7 rule (Empirical Rule) · z-scores · Standard normal distribution
Unit 2 · Exploring Two-Variable Data 探索双变量数据
Exam weight: 5-7%
2.1 — Introducing Statistics: Are Variables Related? 统计学入门：变量之间有关联吗？
· Relationships between variables · Association vs. causation
2.2 — Representing Two Categorical Variables 表示两个分类变量
· Two-way tables · Marginal distributions · Joint distributions
2.3 — Statistics for Two Categorical Variables 两个分类变量的统计量
· Conditional relative frequencies · Simpson's paradox · Association
2.4 — Representing the Relationship Between Two Quantitative Variables 表示两个定量变量之间的关系
· Scatterplots · Direction · Form · Strength
2.5 — Correlation 相关性
· Correlation coefficient r · Properties of correlation · Correlation does not imply causation
2.6 — Linear Regression Models 线性回归模型
· Regression equation · Interpretation of slope and intercept · Prediction
2.7 — Residuals 残差
· Definition of residuals · Residual plots · Residual analysis
2.8 — Least Squares Regression 最小二乘回归
· Least squares method · Coefficient of determination r squared · Properties of the regression line
2.9 — Analyzing Departures from Linearity 分析偏离线性的情况
· Nonlinear patterns · Outliers · High leverage points · Variable transformations
Unit 3 · Collecting Data 收集数据
Exam weight: 12-15%
3.1 — Introducing Statistics: Do the Data We Collected Tell the Truth? 统计学入门：我们收集的数据是否可靠？
· Importance of data collection methods · Sources of bias
3.2 — Introduction to Planning a Study 研究计划导论
· Observational studies · Experiments · Surveys · Census
3.3 — Random Sampling and Data Collection 随机抽样与数据收集
· Simple random sampling · Stratified sampling · Cluster sampling · Systematic sampling
3.4 — Potential Problems with Sampling 抽样的潜在问题
· Sampling bias · Nonresponse bias · Response bias · Convenience sampling
3.5 — Introduction to Experimental Design 实验设计导论
· Treatments · Experimental units · Response variable · Explanatory variable · Control group
3.6 — Selecting an Experimental Design 选择实验设计
· Completely randomized design · Randomized block design · Matched pairs design
3.7 — Inference and Experiments 推断与实验
· Causal inference · Generalization to a population · Role of randomization · Confounding variables
Unit 4 · Probability, Random Variables, and Probability Distributions 概率、随机变量和概率分布
Exam weight: 10-20%
4.1 — Introducing Statistics: Random and Non-Random Patterns? 统计学入门：随机与非随机模式？
· Randomness · Long-run relative frequency · Meaning of probability
4.2 — Estimating Probabilities Using Simulation 使用模拟估计概率
· Simulation methods · Random number tables · Random number generators
4.3 — Introduction to Probability 概率导论
· Sample space · Events · Basic properties of probability · Complement of an event
4.4 — Mutually Exclusive Events 互斥事件
· Definition of mutually exclusive events · Addition rule
4.5 — Conditional Probability 条件概率
· Conditional probability formula · Multiplication rule · Tree diagrams
4.6 — Independent Events and Unions of Events 独立事件与事件的并集
· Independence · General addition rule · Multiplication rule and independence
4.7 — Introduction to Random Variables and Probability Distributions 随机变量和概率分布导论
· Discrete random variables · Continuous random variables · Probability distributions
4.8 — Mean and Standard Deviation of Random Variables 随机变量的均值和标准差
· Expected value · Variance · Standard deviation
4.9 — Combining Random Variables 组合随机变量
· Linear transformations of random variables · Mean and variance of sums of independent random variables
4.10 — Introduction to the Binomial Distribution 二项分布导论
· Binomial experiment · Binomial probability · Conditions for binomial distribution
4.11 — Parameters for a Binomial Distribution 二项分布的参数
· Mean of a binomial distribution · Standard deviation of a binomial distribution
4.12 — The Geometric Distribution 几何分布
· Geometric random variable · Geometric probability · Mean of a geometric distribution
Unit 5 · Sampling Distributions 抽样分布
Exam weight: 7-12%
5.1 — Introducing Statistics: Why Is My Sample Not Like Yours? 统计学入门：为什么我的样本和你的不一样？
· Sampling variability · Statistics and parameters
5.2 — The Normal Distribution Revisited 再探正态分布
· Normal probability calculations · Normal quantiles · Normal probability plot
5.3 — The Central Limit Theorem 中心极限定理
· Central Limit Theorem statement · Effect of sample size · Conditions for approximate normality
5.4 — Biased and Unbiased Point Estimates 有偏和无偏点估计
· Unbiased estimators · Biased estimators · Variability of estimators
5.5 — Sampling Distributions for Sample Proportions 样本比例的抽样分布
· Mean of a sample proportion · Standard deviation of a sample proportion · Conditions for normal approximation
5.6 — Sampling Distributions for Sample Means 样本均值的抽样分布
· Mean of a sample mean · Standard deviation of a sample mean · t-distribution
5.7 — Sampling Distributions for Differences in Sample Proportions 样本比例差的抽样分布
· Mean of a difference of two proportions · Standard deviation of a difference of two proportions · Conditions for testing
5.8 — Sampling Distributions for Differences in Sample Means 样本均值差的抽样分布
· Mean of a difference of two means · Standard deviation of a difference of two means · Degrees of freedom
Unit 6 · Inference for Categorical Data: Proportions 分类数据的推断：比例
Exam weight: 12-15%
6.1 — Introducing Statistics: Why Be Normal? 统计学入门：为什么要正态？
· Concept of inference · Role of normal distribution in inference
6.2 — Constructing a Confidence Interval for a Population Proportion 构建总体比例的置信区间
· Confidence interval formula · Critical value · Standard error · Conditions check
6.3 — Justifying a Claim Based on a Confidence Interval for a Population Proportion 基于总体比例置信区间证明论断
· Interpretation of confidence intervals · Confidence level · Sample size and interval width
6.4 — Setting Up a Test for a Population Proportion 建立总体比例的检验
· Null hypothesis · Alternative hypothesis · Significance level
6.5 — Interpreting p-Values 解释p值
· Definition of p-value · Meaning of p-value · Statistical significance
6.6 — Concluding a Test for a Population Proportion 完成总体比例的检验
· Reject or fail to reject the null hypothesis · Stating conclusions · Conditions for the test
6.7 — Potential Errors When Performing Tests 假设检验中的潜在错误
· Type I error · Type II error · Power of a test
6.8 — Confidence Intervals for the Difference of Two Proportions 两个比例差的置信区间
· Confidence interval formula for the difference of two proportions · Standard error · Conditions check
6.9 — Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions 基于总体比例差置信区间证明论断
· Interpretation when interval contains zero · Practical vs. statistical difference
6.10 — Setting Up a Test for the Difference of Two Population Proportions 建立两个总体比例差的检验
· Pooled proportion · Setting up hypotheses · Test statistic
6.11 — Carrying Out a Test for the Difference of Two Population Proportions 执行两个总体比例差的检验
· z-test statistic · p-value calculation · Stating conclusions
Unit 7 · Inference for Quantitative Data: Means 定量数据的推断：均值
Exam weight: 10-18%
7.1 — Introducing Statistics: Should I Worry About Error? 统计学入门：我应该担心误差吗？
· Sources of error · Sampling error vs. non-sampling error
7.2 — Constructing a Confidence Interval for a Population Mean 构建总体均值的置信区间
· t-interval formula · t-distribution · Degrees of freedom · Conditions check
7.3 — Justifying a Claim Based on a Confidence Interval for a Population Mean 基于总体均值置信区间证明论断
· Interpretation of confidence intervals · Capture rate · Determining sample size
7.4 — Setting Up a Test for a Population Mean 建立总体均值的检验
· Hypotheses for t-tests · One-sided and two-sided tests · Conditions check
7.5 — Carrying Out a Test for a Population Mean 执行总体均值的检验
· t-test statistic · p-value · Stating conclusions
7.6 — Confidence Intervals for the Difference of Two Population Means 两个总体均值差的置信区间
· Two-sample t-interval · Standard error · Degrees of freedom
7.7 — Justifying a Claim Based on a Confidence Interval for a Difference of Population Means 基于总体均值差置信区间证明论断
· Interpretation of the interval · Significance of the difference
7.8 — Setting Up a Test for the Difference of Two Population Means 建立两个总体均值差的检验
· Hypotheses for two-sample t-tests · Independence condition · Normality condition
7.9 — Carrying Out a Test for the Difference of Two Population Means 执行两个总体均值差的检验
· Two-sample t-test statistic · p-value · Conclusions
7.10 — Skills Focus: Selecting, Implementing, and Communicating Inference Procedures 技能聚焦：选择、实施和交流推断程序
· Choosing appropriate inference procedures · Checking conditions · Interpreting results
Unit 8 · Inference for Categorical Data: Chi-Square 分类数据的推断：卡方
Exam weight: 2-5%
8.1 — Introducing Statistics: Could It Just Be by Chance? 统计学入门：这可能只是巧合吗？
· Motivation for chi-square tests · Observed and expected counts
8.2 — Setting Up a Chi-Square Goodness of Fit Test 建立卡方拟合优度检验
· Setting up hypotheses · Calculating expected counts · Conditions check
8.3 — Carrying Out a Chi-Square Goodness of Fit Test 执行卡方拟合优度检验
· Chi-square statistic · Degrees of freedom · p-value · Conclusions
8.4 — Expected Counts in Two-Way Tables 双向表中的期望频数
· Expected count formula · Row and column totals
8.5 — Setting Up a Chi-Square Test for Homogeneity or Independence 建立齐性或独立性卡方检验
· Test for homogeneity · Test for independence · Distinguishing hypotheses
8.6 — Carrying Out a Chi-Square Test for Homogeneity or Independence 执行齐性或独立性卡方检验
· Calculating chi-square statistic · Degrees of freedom · Stating conclusions
Unit 9 · Inference for Quantitative Data: Slopes 定量数据的推断：斜率
Exam weight: 2-5%
9.1 — Introducing Statistics: Do Those Points Predict Anything? 统计学入门：这些点能预测什么吗？
· Motivation for regression inference · Population regression line
9.2 — Confidence Intervals for the Slope of a Regression Model 回归模型斜率的置信区间
· Standard error of the slope · t-interval · Conditions check
9.3 — Setting Up a Test for the Slope of a Regression Model 建立回归模型斜率的检验
· Setting up hypotheses · Testing for linear relationship · Conditions
9.4 — Carrying Out a Test for the Slope of a Regression Model 执行回归模型斜率的检验
· t-test statistic · p-value · Interpreting computer output
9.5 — Confidence Intervals for the Slope of a Regression Model 回归模型斜率的置信区间（续）
· Constructing and interpreting confidence intervals · Relationship with hypothesis testing