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AP Statistics

One lesson for each of the course’s 55 topics, in the order the course teaches them. The first 2 units are free for everyone; the rest come with the AP Statistics plan. Read a lesson, try its quick checks, then practice the topic with exam-style questions.

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Exploring One-Variable Data and Collecting Data

Unit 1Free13 lessons
  1. 1.1Introducing Statistics: What Can We Learn from Data?Name the population, sample, N and n in any study, explain why a sample is used, and judge whether an investigative question can actually be answered.
  2. 1.2VariablesIdentify the observational units and variables in a study, classify each variable as categorical, discrete or continuous, and tell a parameter from a statistic.
  3. 1.3Tabular Representation and Summary Statistics for One Categorical VariableBuild frequency and relative frequency tables for a categorical variable, move between counts, proportions, percents and ratios, and use them to back a claim.
  4. 1.4Graphical Representations for One Categorical VariableDraw bar charts and pie charts for a categorical variable, use them to justify claims in context, and compare groups of different sizes without being misled.
  5. 1.5Graphical Representations for One Quantitative VariableConstruct dotplots, stem-and-leaf plots and histograms for a quantitative variable, choose sensible bins, and read exactly what each graph can and cannot tell you.
  6. 1.6Descriptions for One Quantitative Variable DistributionsDescribe a histogram, dotplot or stemplot by its shape, center, spread and unusual features in context, and use the graph to support or refute a claim.
  7. 1.7Summary Statistics for One Quantitative VariableCalculate and interpret the mean, median, quartiles, percentiles, range, IQR and standard deviation, flag outliers, and choose the right summary for skewed data.
  8. 1.8Graphical Representations of Summary Statistics for One Quantitative VariableBuild a boxplot from a five-number summary with outliers marked, read shape and percentages from it, and connect skew to where the mean falls relative to the median.
  9. 1.9Comparisons of the Distributions for One Quantitative VariableCompare two or more distributions by shape, center, variability and unusual features, justify claims from the comparison, and compare relative positions with z-scores.
  10. 1.10The Investigative Question Revisited and Data CollectionWrite a complete investigative question, tell censuses, experiments and observational studies apart, spot confounding, and judge the scope of conclusions.
  11. 1.11Random SamplingIdentify simple random, stratified, cluster and systematic samples, describe how to select each, and justify which one fits a study.
  12. 1.12Potential Problems with SamplingRecognize voluntary response, undercoverage, nonresponse and response bias, and explain in context which way each one pushes an estimate.
  13. 1.13Experimental DesignIdentify the parts of a well-designed experiment, describe completely randomized, block and matched pairs designs, and justify cause-and-effect conclusions.

Probability, Random Variables, and Probability Distributions

Unit 2Free12 lessons
  1. 2.1Tabular and Graphical Representations for the Distributions of Two Categorical VariablesRead two-way tables, side-by-side and segmented bar charts and mosaic plots, and use them to decide and justify whether two categorical variables are associated.
  2. 2.2Summary Statistics for Two Categorical VariablesCalculate joint, marginal and conditional relative frequencies from a two-way table, pick the one a question asks for, and use them to justify a claim of association.
  3. 2.3Estimating Probabilities Using SimulationDesign and carry out a simulation with random digits or a random number generator, estimate a probability from it, and explain what the law of large numbers promises.
  4. 2.4Introduction to ProbabilityList a sample space, find probabilities by counting equally likely outcomes, check a probability model, and use the complement rule for "not" and "at least one".
  5. 2.5Mutually Exclusive EventsFind the probability that two events both happen, read it from a table or a description, and use it to justify whether two events are mutually exclusive.
  6. 2.6Conditional ProbabilityCompute a probability given that another event happened, from a two-way table, a tree diagram, or the formula, and use the general multiplication rule.
  7. 2.7Independent Events and Unions of EventsDecide whether two events are independent, find the probability that both occur when they are, and find the probability that one or the other occurs.
  8. 2.8Introduction to Random Variables and Probability DistributionsDefine a discrete random variable, build its probability distribution from probability rules or a simulation, and read and use its cumulative distribution.
  9. 2.9Parameters of Random VariablesCalculate the mean (expected value) and standard deviation of a discrete random variable and interpret both in context as long-run quantities.
  10. 2.10The Binomial DistributionDecide whether a count is binomial, then find binomial probabilities, the mean np and the standard deviation, and interpret them in context.
  11. 2.11The Normal DistributionDescribe a normal distribution, use the empirical rule and z-scores to find areas and cutoffs, and compare positions within and between normal distributions.
  12. 2.12Sampling Distributions and the Central Limit TheoremDescribe the sampling distribution of a statistic, simulate one or re-randomize an experiment, and explain what the central limit theorem says about sample means.

Inference for Categorical Data: Proportions

Unit 3With the plan15 lessons
  1. 3.1EstimatorsTurn sample data into estimates of a population parameter, and justify from a sampling distribution whether an estimator is unbiased.
  2. 3.2Sampling Distributions for Sample ProportionsFind and interpret the mean and standard deviation of the sampling distribution of a sample proportion, check its conditions, and compute probabilities from it.
  3. 3.3Constructing a Confidence Interval for a Population ProportionBuild a one-sample z-interval for a population proportion: define the parameter, check the conditions, compute the margin of error, and choose a sample size.
  4. 3.4Justifying a Claim Based on a Confidence Interval for a Population ProportionInterpret a confidence interval and its confidence level for a proportion in context, judge a claim with it, and predict what changes its width.
  5. 3.5Setting Up a Test for a Population ProportionSet up a one-sample z-test for a population proportion: define the parameter, write null and alternative hypotheses, and check the conditions using the null value.
  6. 3.6p-ValuesFind which tail of the null distribution a p-value is, compute it for a one- or two-sided alternative, and interpret it in context the way graders require.
  7. 3.7Carrying Out a Test for a Population ProportionCompute the z statistic and p-value for a one-sample z-test for a proportion, compare the p-value with alpha, and write a conclusion in context that earns full credit.
  8. 3.8Potential Errors When Performing TestsIdentify and describe Type I and Type II errors in context, find their probabilities from alpha and power, and explain what changes the power of a test.
  9. 3.9Sampling Distributions for the Difference Between Sample ProportionsFind the mean and standard deviation of the difference between two sample proportions, check the conditions behind them, and use a normal model for probabilities.
  10. 3.10Constructing a Confidence Interval for the Difference Between Two Population ProportionsIdentify a two-sample z-interval for p1 minus p2, define its parameter in context, check its three conditions, and compute the interval by hand or with technology.
  11. 3.11Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population ProportionsInterpret a confidence interval and confidence level for p1 - p2 in context, and use the interval to decide whether it supports a claim about two groups.
  12. 3.12Setting Up a Test for the Difference Between Two Population ProportionsRecognize when a two-sample z-test for p1 - p2 fits, define its parameters, write the hypotheses, and check the random, 10% and large counts conditions.
  13. 3.13Carrying Out a Test for the Difference Between Two Population ProportionsCompute the pooled z statistic and p-value for p1 - p2, interpret the p-value assuming equal proportions, and write the conclusion in context.
  14. 3.14Setting Up a Chi-Square Test for Homogeneity or IndependenceTell a chi-square test for homogeneity from one for independence, state its hypotheses in context, check its conditions, and describe chi-square distributions.
  15. 3.15Carrying Out a Chi-Square Test for Homogeneity or IndependenceCompute expected counts, the chi-square statistic, degrees of freedom and p-value for a two-way table, then interpret the p-value and state the conclusion in context.

Inference for Quantitative Data: Means

Unit 4With the plan10 lessons
  1. 4.1Sampling Distributions for Sample MeansFind the mean and standard deviation of the sampling distribution of a sample mean, decide when it is approximately normal, and compute probabilities for it.
  2. 4.2Constructing a Confidence Interval for a Population Mean or Population Mean DifferenceBuild a one-sample t-interval for a population mean or a matched-pairs mean difference, from choosing the critical value and checking conditions to the final interval.
  3. 4.3Justifying a Claim Based on a Confidence Interval for a Population Mean or Population Mean DifferenceInterpret a t-interval and its confidence level in context, use the interval to judge a claim about a mean or mean difference, and predict how its width changes.
  4. 4.4Setting Up a Test for a Population Mean or Population Mean DifferenceChoose a one-sample t-test for a mean or a matched-pairs mean difference, define the parameter, write the hypotheses, and check the conditions.
  5. 4.5Carrying Out a Test for a Population Mean or Population Mean DifferenceCompute the t statistic and p-value for a one-sample or matched-pairs t-test, interpret the p-value, and state a conclusion in context.
  6. 4.6Sampling Distributions for the Difference Between Two Sample MeansFind the mean and standard deviation of the difference between two sample means, check when a normal model fits it, and use it to find probabilities.
  7. 4.7Constructing a Confidence Interval for the Difference Between Two Population MeansName the parameter, check the three conditions, and build a two-sample t-interval for a difference in population means, by hand and by calculator.
  8. 4.8Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population MeansInterpret a two-sample t-interval and its confidence level in context, and use the interval to decide whether a claim about two means is supported.
  9. 4.9Setting Up a Test for the Difference Between Two Population MeansChoose a two-sample t-test, define the two population means in context, write the hypotheses, and check the conditions before any calculation.
  10. 4.10Carrying Out a Test for the Difference Between Two Population MeansCompute the two-sample t statistic and p-value, interpret the p-value in context, and state a conclusion about two population means at a given significance level.

Regression Analysis

Unit 5With the plan5 lessons
  1. 5.1Graphical Representations Between Two Quantitative VariablesBuild a scatterplot with the right variable on each axis, then describe the association by its direction, form, strength and unusual features, in context.
  2. 5.2CorrelationInterpret the correlation r for a linear relationship, know what changes it and what can't, and explain why a strong r proves neither a line nor a cause.
  3. 5.3Linear Regression ModelsUse a regression equation to predict a response from an explanatory value, read its notation correctly, and judge when a prediction is an extrapolation.
  4. 5.4ResidualsCompute a residual, say in context whether the model overpredicted or underpredicted, and use a residual plot to decide whether a linear model fits.
  5. 5.5Least-Squares RegressionFind the least-squares line with technology, know why it is the best fit, and interpret its slope, intercept, and r squared in context the way graders expect.

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