AP Statistics Syllabus



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 |Assignment/Project |

|1.1 |Construct and interpret graphical displays of distributions of univariate data (dotplot, stemplot, |Technology: Finding Calculator | |

|Displaying Distributions w/Graphs|histogram, cumulative frequency plot) |Histograms on | |

| |1. Center and spread |TI-83/84 | |

| |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 | | |

|1.2 |Summarize distributions of univariate data |Technology: Finding Calculator| |

|Describing Distributions w/ |1. Measuring center: median, mean |boxplots, mean, standard | |

|Numbers |2. Measuring spread: range, interquartile range, standard deviation |deviation and five number | |

| |3. Measuring position: quartiles, percentiles, standardized scores (z-scores) |summary on | |

| |4. Using boxplots |TI-83/84 | |

| |5. The effect of changing units on summary measures | | |

|Chapter Review | | | |

|Test 1 | | | |

Chapter 2 – The Normal Distribution

|Section |Outcomes/Objectives |Technology |Assignment/Project |

|2.1 |Use a normal distribution as an approximation top the overall pattern of data. | | |

|Density Curves and the Normal |1. Know properties of the normal distribution | | |

|Distribution | | | |

|2.2 |Calculate specified areas under the normal curve. |Technology: Normal Probability| |

|Standard Normal Calculations |Use a normal distribution table and calculator to calculate proportions of values above, below and between two |Plots, area, and z values on | |

| |numbers. |TI-83/84 | |

| |Use a normal distribution table and calculator to calculate the point having a stated proportions of values | | |

| |above and below it | | |

|Chapter Review | | | |

|Test 2 | | | |

Chapter 4 –

|Section |Outcomes/Objectives |Technology |Assignment/Project |

| | | | |

|4.2 |Interpret correlation and regression | | |

|Cautions about Correlation and |1. Understand the effects of extreme observations | | |

|Regression |2. Recognize lurking variables | | |

| |3. Understand the difference between a strong correlation and cause-and-effect relationships | | |

|4.3 |Recognize relationships in categorical data | | |

|Relations 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 |Technology |Assignment/Project |

|5.1 |Know methods of data collection | | |

|Designing Samples |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 | | |

|5.2 |Plan and conduct experiments | | |

|Designing 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 |Construct and run a simulation | | |

|Simulating Experiments | | | |

|Chapter Review | | | |

|Test 5 | | | |

III. Anticipating Patterns: Exploring random phenomena using probability and simulation (20%–30%)

Chapter 6 – Probability

|Section |Outcomes/Objectives |Technology |Assignment/Project |

|6.1 |Calculate the probability of random events | | |

|The Idea of Probability |1. Interpret probability, including long-run relative frequency interpretation | | |

|6.2 |Know probability rules and be able to apply them to determine probabilities of defined events | | |

|Probability Models |1. Use addition rule, multiplication rule to find probability of events | | |

| |2. Understand independence versus dependence | | |

|6.3 |Use probability rules to compute probability of events | | |

|General Probability Rules |1. Use general addition rule, multiplication rule, conditional probability rules, and independence to find | | |

| |probability of events | | |

|Chapter Review | | | |

|Test 6 | | | |

Chapter 7 – Random variables

|Section |Outcomes/Objectives |Technology |Assignment/Project |

|7.1 |Recognize and define discrete and continuous random variables | | |

|Discrete and Continuous Random |1.Construct a probability distribution table and a probability histogram for the random variable | | |

|Variables |2. Determine probabilities of events as areas under density curves | | |

|7.2 |Combine independent random variables | | |

|Means and Variances of Random |1. Calculate the mean and variance of a discrete random variable | | |

|Variables |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 |Assignment/Project |

|8.1 |Calculate probability of binomial random variables |Technology: Binomial | |

|The Binomial Distributions |1. Identify a random variable as binomial by verifying four conditions |distributions on TI-83/84 | |

| |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 | | |

|8.2 |Calculate probability of geometric random variables |Technology: Geometric | |

|The Geometric Distributions |1. Identify a random variable as geometric by verifying four conditions |Distributions on TI-83/84 | |

| |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. | | |

|Chapter Review | | | |

|Test 8 | | | |

IV. Statistical Inference: Estimating population parameters and testing hypotheses (30%–40%)

Chapter 9 –Sampling Distributions

|Section |Outcomes/Objectives |Technology |Assignment/Project |

|9.1 |Sampling distributions | | |

|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 | | |

|9.2 |Sampling distributions | | |

|Sample Proportions |1. Recognize when a problem involves a sample proportion | | |

| |2. Find the mean and standard deviation of the sampling distribution of a sample proportion | | |

|9.3 |Sampling distributions | | |

|Sample Means |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 |Assignment/Project |

|3.1 |Explore bivariate data |Technology: Scatterplots on | |

|Scatterplots |Construct scatterplots |TI-83/84 | |

| |Analyze patterns in scatterplots | | |

|3.2 |Explore bivariate data |Technology: Finding LSRL on | |

|Correlation |1. Know properties of and calculate the correlation between two quantitative variables |TI-83/84 | |

|3.3 |Explore bivariate data |Technology: Finding Residuals | |

|Least-Squares Regression |1. Find the least-squares regression line |on TI-83/84 | |

| |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 | | |

|Chapter Review | | | |

|Test 3 | | | |

|4.1 |Model nonlinear data | | |

|Transforming Relationships |1. Use transformations to achieve linearity: logarithmic and power | | |

| |transformations | | |

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