AP Statistics

1. Getting Started

1.1 What is Statistics?

1.2 Random Samples: Levels of Measurement, Simple Random Samples, Other Sampling Techniques

1.3 Introductions to Experimental Design

2. Organizing Data

2.1 Bar Graphs, Pareto Charts, Circle Graphs, and Time-Series Graphs

2.2 Histograms, Frequency Distributions, Frequency Polygons and Ogives

2.3 Stem-and-Leaf Displays

3. Averages and Variation

3.1 Measures of Central Tendency: Mode, Median, Mean, and Weighted Averages

3,2 Chebyshev's Theorem, Measures of Variation, Coefficient of Variation

3.3 Mean and Standard Deviation of Grouped Data, Coefficient of Variation for Grouped Data

3.4 Percentiles and Box-and-Whisker Plots

4. Elementary Probability Theory

4.1 What Is Probability? Probability and Statistics

4.2 Probability Rules for Compound Events: Multiplication Rule, Addition Rule, Contingency Tables

4.3 Trees and Counting Techniques, Permutations, Combinations

5. The Binomial Probability Distribution and Related Topics

5.1 Introduction to Random Variables and Probability Distributions

5.2 Binomial Experiments, Binomial Probabilities, Binomial Probabilities

5.3 Additional Properties of the Binomial Distribution. Mean-Standard Deviation. Quota Problems

5.4 The Geometric Probability Distributions

6. The Normal Distribution

6.1 Graphs of Normal Probability Distributions, Control Charts

6.2 Standard Units and Areas Under the Standard Normal Distribution

6.3 Areas Under Any Normal Curve. The Inverse Normal Distribution

6.4 Normal Approximation to the Binomial Distribution

7. Introduction to Sampling Distributions

7.1 Sampling Distributions

7.2 The Central Limit Theorem, The Central Limit Theorem for No-Normal Distributions

7.3 Sampling Distributions for Proportions. Control Chart for Proportions

8. Estimation

8.1 Estimating Mean when Standard Deviation is Known. Margin of Error-Confidence Intervals

8.2 Estimating Mean when Standard Deviation is Unknown: The T-Distribution. Confidence intervals

8.3 Estimating p in the Binomial Distribution

8.4 Choosing a Sample Size

8.5 Estimating m₁ - m₂ when SD is Known, Estimating m₁ - m₂ when SD is Unknown, and Estimating p₁ - p₂

9. Hypothesis Testing

9.1 Introduction to Statistical Tests; P-value, Hypothesis Testing

9.2 Testing the Mean when SD is Known. Testing the Mean when SD is Unknown

9.3 Testing a Proportion

9.4 Dependent Samples. Tests Involving Paired Differences

9.5 Independent Samples. Testing m₁ - m₂ SD Known, Testing m₁ - m₂ SD Unknown, Testing p₁ - p₂

10. Correlation and Regression

10.1 Scatter Diagrams and Linear Correlation. The Correlation Coefficient

10.2 Linear Regression and the Coefficient of Determination

10.3 Inferences for Correlation and Regression: The Standard Error, Testing the Coefficient of Correlation, Inferences about Slope.

11. Chi-Square Distribution

11.1 The Chi-Square Distribution. Tests of Independence

11.2 Chi-Square: Goodness of Fit