AP Statistics Cheat Sheet

At examples.com, we provide a comprehensive AP Statistics cheat sheet covering essential topics like probability, sampling distributions, and regression models, designed to help students excel in their exams.

Free AP Statistics Practice Test

Unit 1: Exploring One-Variable Data

Variation in categorical and quantitative variables: Understand the difference between categorical and quantitative data and how variation occurs in each.
Representing data using tables or graphs: Use tables, bar charts, histograms, dot plots, and box plots to represent data visually.
Calculating and interpreting statistics: Calculate measures of central tendency (mean, median, mode) and spread (range, IQR, standard deviation).
Describing and comparing distributions of data: Use terms like shape, center, spread, and outliers to describe distributions.
The normal distribution: Recognize and use the properties of the normal distribution, including empirical rule (68-95-99.7%).

Unit 2: Exploring Two-Variable Data

Comparing representations of 2 categorical variables: Use two-way tables and segmented bar charts to compare categorical variables.
Calculating statistics for 2 categorical variables: Calculate and interpret marginal and joint probabilities.
Representing bivariate quantitative data using scatter plots: Plot and interpret scatter plots to explore relationships between two quantitative variables.
Describing associations in bivariate data and interpreting correlation: Describe associations using direction, form, and strength; interpret the correlation coefficient (r).
Linear regression models: Fit a linear model to data and interpret the slope and y-intercept in context.
Residuals and residual plots: Analyze residuals to assess the fit of a linear model.
Departures from linearity: Identify and describe non-linear patterns in data.

Unit 3: Collecting Data

Planning a study: Develop a plan for collecting data, including defining the population and sampling methods.
Sampling methods: Understand simple random sampling, stratified sampling, and cluster sampling.
Sources of bias in sampling methods: Identify and describe potential biases, including undercoverage, nonresponse, and voluntary response bias.
Designing an experiment: Distinguish between observational studies and experiments; understand random assignment and control.
Interpreting the results of an experiment: Draw valid conclusions based on experiment design, considering causality and generalizability.

Unit 4: Probability, Random Variables, and Probability Distributions

Using simulation to estimate probabilities: Use random simulations to estimate the likelihood of events.
Calculating the probability of a random event: Apply probability rules, including addition and multiplication rules, to calculate event probabilities.
Random variables and probability distributions: Understand discrete and continuous random variables and their probability distributions.
The binomial distribution: Recognize and apply the binomial probability formula.
The geometric distribution: Calculate probabilities using the geometric distribution for trials until the first success.

Unit 5: Sampling Distributions

Variation in statistics for samples collected from the same population: Understand how sample statistics vary and how they relate to the population parameters.
The central limit theorem: Use the CLT to justify that sampling distributions of the sample mean are approximately normal for large sample sizes.
Biased and unbiased point estimates: Distinguish between biased and unbiased estimators.
Sampling distributions for sample proportions: Describe and calculate standard error for sampling distributions of sample proportions.
Sampling distributions for sample means: Understand and calculate the standard error for sampling distributions of sample means.

Unit 6: Inference for Categorical Data: Proportions

Constructing and interpreting a confidence interval for a population proportion: Use sample data to construct confidence intervals for population proportions.
Setting up and carrying out a test for a population proportion: Perform hypothesis tests for population proportions, interpreting p-values correctly.
Interpreting a p-value and justifying a claim about a population proportion: Use p-values to make decisions about population proportions.
Type I and Type II errors in significance testing: Understand and differentiate between Type I and Type II errors.
Confidence intervals and tests for the difference of 2 proportions: Construct and interpret confidence intervals and tests for comparing two population proportions.

Unit 7: Inference for Quantitative Data: Means

Constructing and interpreting a confidence interval for a population mean: Calculate confidence intervals for means using sample data.
Setting up and carrying out a test for a population mean: Conduct hypothesis tests for population means.
Interpreting a p-value and justifying a claim about a population mean: Use p-values to justify claims about population means.
Confidence intervals and tests for the difference of 2 population means: Compare two population means using confidence intervals and hypothesis tests.

Unit 8: Inference for Categorical Data: Chi-Square

The chi-square test for goodness of fit: Test how well observed categorical data fit an expected distribution.
The chi-square test for homogeneity: Compare distributions of categorical variables across different populations.
The chi-square test for independence: Assess whether two categorical variables are independent.
Selecting an appropriate inference procedure for categorical data: Choose the correct test (goodness of fit, homogeneity, independence) based on the context.

Unit 9: Inference for Quantitative Data: Slopes

Confidence intervals for the slope of a regression model: Construct and interpret confidence intervals for the slope of a regression line.
Setting up and carrying out a test for the slope of a regression model: Perform hypothesis tests for the slope, interpreting the significance of the relationship.
Selecting an appropriate inference procedure: Choose the right test or confidence interval based on the data type and research question.