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AP Statistics Course Outline 2011-2012 I. Exploring Data: Describing patterns and departures from patterns (20%–30%) Chapter 1 – Exploring Data Section Outcomes/Objectives Technology 1.1 Displaying Distributions w/Graphs Construct and interpret graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) 1. Center and spread 2. Clusters and gaps 3. Outliers and other unusual features 4. Shape Compare distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) 1. Compare center and spread: within groups, between groups variation 2. Compare clusters and gaps 3. Compare outliers and other unusual features 4. Compare shapes Technology: Finding Calculator Histograms on TI-83/84 1.2 Describing Distributions w/ Numbers Summarize distributions of univariate data 1. Measuring center: median, mean 2. Measuring spread: range, interquartile range, standard deviation 3. Measuring position: quartiles, percentiles, standardized scores (z-scores) 4. Using boxplots 5. The effect of changing units on summary measures Technology: Finding Calculator boxplots, mean, standard deviation and five number summary on TI-83/84 Assignment/Project Chapter Review Test 1 Chapter 2 – The Normal Distribution Section Outcomes/Objectives 2.1 Density Curves and the Normal Distribution 2.2 Standard Normal Calculations Technology Use a normal distribution as an approximation top the overall pattern of data. 1. Know properties of the normal distribution Calculate specified areas under the normal curve. 1. Use a normal distribution table and calculator to calculate proportions of values above, below and between two numbers. 2. Use a normal distribution table and calculator to calculate the point having a stated proportions of values above and below it Technology: Normal Probability Plots, area, and z values on TI83/84 Assignment/Project Chapter Review Test 2 Chapter 4 – Section 4.2 Cautions about Correlation and Regression 4.3 Relations in Categorical Data Outcomes/Objectives Technology Assignment/Project Interpret correlation and regression 1. Understand the effects of extreme observations 2. Recognize lurking variables 3. Understand the difference between a strong correlation and cause-and-effect relationships Recognize relationships in categorical data 1. Construct frequency tables and bar charts 2. Find marginal and joint frequencies for two-way tables 3. Describe the relationship between two categorical variables by computing and comparing percents 4. Compare distributions using bar charts Chapter Review Test 4 II. Sampling and Experimentation: Planning and conducting a study (10%–15%) Chapter 5 – Producing Data Section Outcomes/Objectives 5.1 Designing Samples Know methods of data collection 1. Census 2. Sample survey 3. Experiment 4. Observational study Plan and conduct surveys 1. Know characteristics of a well-designed and well-conducted survey 2. Use random tables or random digits to select a simple random sample (SRS) 3. Recognize sources of bias in sampling and surveys 4. Sampling methods, including simple random sampling, stratified random sampling, and cluster sampling Generalize results and types of conclusions that can be drawn from observational studies, experiments, and surveys Technology Assignment/Project 5.2 Designing Experiments Plan and conduct experiments 1. Know characteristics of a well-designed and well-conducted experiment 2. Outline a completely randomized design (including treatments, control groups, experimental units, random assignments, and replication) 3. Recognize sources of bias and confounding, including placebo effect and blinding Generalize results and types of conclusions that can be drawn from observational studies, experiments, and surveys 5.3 Simulating Experiments Construct and run a simulation Chapter Review Test 5 III. Anticipating Patterns: Exploring random phenomena using probability and simulation (20%–30%) Chapter 6 – Probability Section Outcomes/Objectives 6.1 The Idea of Probability 6.2 Probability Models Calculate the probability of random events 1. Interpret probability, including long-run relative frequency interpretation 6.3 General Probability Rules Use probability rules to compute probability of events 1. Use general addition rule, multiplication rule, conditional probability rules, and independence to find probability of events Technology Assignment/Project Technology Assignment/Project Know probability rules and be able to apply them to determine probabilities of defined events 1. Use addition rule, multiplication rule to find probability of events 2. Understand independence versus dependence Chapter Review Test 6 Chapter 7 – Random variables Section Outcomes/Objectives 7.1 Discrete and Recognize and define discrete and continuous random variables 1.Construct a probability distribution table and a probability histogram for the random Continuous Random Variables variable 2. Determine probabilities of events as areas under density curves 7.2 Means and Variances of Random Variables Combine independent random variables 1. Calculate the mean and variance of a discrete random variable 2. Use simulation methods and the law of large numbers to approximate the mean of a distribution 3. Use rules for means and variances to solve problems involving sums, differences, and linear combinations of random variables Chapter Review Test 7 Chapter 8 – The Binomial and Geometric Distributions Section Outcomes/Objectives Technology 8.1 The Binomial Distributions Calculate probability of binomial random variables 1. Identify a random variable as binomial by verifying four conditions 2. Use calculator or formula to determine binomial probabilities and construct probability distribution tables and histograms 3. Calculate cumulative distribution functions and construct cumulative distribution tables and histograms 4. Calculate means and standard deviations of binomial random variables. 5. Use a normal approximation to the binomial distribution to compute probabilities Technology: Binomial distributions on TI-83/84 8.2 The Geometric Distributions Calculate probability of geometric random variables 1. Identify a random variable as geometric by verifying four conditions 2. Use calculator or formula to determine geometric probabilities and construct probability distribution tables and histograms 3. Calculate cumulative distribution functions and construct cumulative distribution tables and histograms 4. Calculate means and standard deviations of geometric random variables. Technology: Geometric Distributions on TI83/84 Assignment/Project Chapter Review Test 8 IV. Statistical Inference: Estimating population parameters and testing hypotheses (30%–40%) Chapter 9 –Sampling Distributions Section Outcomes/Objectives 9.1 Sampling Distributions 9.2 Sample Proportions 9.3 Sample Means Technology Assignment/Project Sampling distributions 1. Identify parameters and statistics in a sample or experiment 2. Interpret a sampling distribution 3. Describe the bias and variability of a statistic in terms of the mean and spread of its sampling distribution Sampling distributions 1. Recognize when a problem involves a sample proportion 2. Find the mean and standard deviation of the sampling distribution of a sample proportion Sampling distributions 1. Recognize when a problem involves a sample mean 2. Find the mean and standard deviation of the sampling distribution of a sample mean Chapter Review Test 9 Semester 1 Exam Chapter 3 – Examining Relationships Section Outcomes/Objectives Technology 3.1 Scatterplots Explore bivariate data 1. Construct scatterplots 2. Analyze patterns in scatterplots Technology: Scatterplots on TI-83/84 3.2 Correlation Explore bivariate data 1. Know properties of and calculate the correlation between two quantitative variables Technology: Finding LSRL on TI-83/84 3.3 Least-Squares Regression Explore bivariate data 1. Find the least-squares regression line 2. Find slope and intercept of LSRL. 3. Use regression line to make predictions 4. Use coefficient of determination to describe how much of the variation in one variable can be accounted for by a straight-line relationship with another variable. 5. Calculate the residuals and recognize outliers and influential points Technology: Finding Residuals on TI-83/84 Chapter Review Test 3 Assignment/Project 4.1 Transforming Relationships Model nonlinear data 1. Use transformations to achieve linearity: logarithmic and power transformations