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AP Statistics The entire class is built on the idea that if you want to complete a statistics problem you must think like a statistician. According to LMU faculty, this means going through the following steps: Stats Method 1. 2. 3. 4. Ask a QUESTION about a population COLLECT data ANALYZE the data using appropriate numerical or graphical methods INTERPRET results in the context of the question Standards are from the AP Statistics Course Description pdf pages 11-14. Standards are from the California Common Core State Standards pages 121-122. Unit 1: Stats Method (introduction to) • Simulation IIIA5 o Tables of random digits o RandInt (83-84) & rand (89) o Suggestion: use simulation to solve probability problems similar to topics they have seen in prior classes. • Properties of Random Variables IIIA6 o Linear Combinations of RVs IIB o Focus on Discrete RVs: Binomial & Geometric RVs IIIA4 3.0 • Categorical Data IE o Definition (v. Quantitative Data) o Graphical representations of Categorical Data Unit 2: Collect Data • Sampling v. Experiments v. Observational Studies IIA o Identifying when to use each o Pros & Cons of each in a particular context • Sampling Methods IIB o Unbiased methods: SRS, Stratified RS, Cluster RS o Biased methods: Convenience, Voluntary Response • Experimental Design IIC o Basic design, including proper randomization. o Blocking • Sampling Distributions IIID 15.0, 16.0 o Name different types of RVs with their graphical representations where appropriate 7.0 o Conditions for each different RV (begin inference cheat sheet) o Formulas for µx and σx. 5.0, 6.0 Unit 3: Normal Distribution IIIC 4.0, 7.0, 8.0 © ESHS (Munger), 7-18-14 Note: this is a continuation of the Collect Data and Sampling Distributions topic with special focus on what is arguably the most important sampling distribution in this class. • Graphing Normal Distributions o Standard Normal N(0, 1) o Graphing N(µ,σ) o Use the z-score to transform N(µ,σ) to N(0, 1) • Areas & Percentiles o Explain why P(x < k) is the area it is on a graph (link to geometric probability: since this is a sampling distribution the denominator is one) o Given a P(x < k) or similar statement, students correctly shade a graph o Compute P(x < k) or similar statements using both calculator and z-score/table o Given P(x < k) = m, correctly use calculator (invNorm) or z-score/table to find k. • 65-95-99.7 rule o Happens after above so that students understand it is a special case o Present as a shortcut Unit 4: Analyze and Interpret Univariate Data Note: this is a long unit and 30%-40% of the AP exam is about inference. Schedule/emphasize appropriately. • Construct, Interpret & Compare Graphical Displays of Univariate Data IABC o Given a set of data compute the numerical descriptors of center (mean, median, mode), spread (standard deviation, IQR, range) and shape (outliers) 10.0, 11.0 o When to use mean/standard deviation v. median/IQR o Construct stem & leaf, boxplots, histograms and how to decide which is appropriate in a given context 14.0 o Given a graph, describe its SOCS (shape, outliers, center spread). o Given two graphs, compare/contrast them in context (SOCS in context) • Inference: Confidence Intervals IVA o Work on inference cheat sheet • Inference: Hypothesis Tests IVB o Complete inference cheat sheet Unit 5: Analyze & Interpret Bivariate Data • Create & Interpret Scatterplots ID1 o Form, direction, strength o Causation v. Correlation • Compute LSRL equation ID2,3 o Compute and interpret correlation coefficient and coefficient of determination 12.0 o Explain slope and y-intercept of LSRL equation in context o Use LSRL to extrapolate; constraints on extrapolation • Residuals ID4 o Show residuals on scatterplot and residual graph o Create & interpret residual plot • Transformations to include linearity: logarithmic and power transformations ID5 (this is a topic I skipped this year since it is rarely on the exam) © ESHS (Munger), 7-18-14 Unit 6: Classical Probability • Interpreting probability IIIA1 3.0 • Law of Large Numbers IIIA2 • Rules: addition rule, multiplication rule, conditional probability and independence IIIA3 1.0, 2.0 © ESHS (Munger), 7-18-14