This is an Outline of a General Advance-Placement (AP) Statistics Curriculum
Outline
Each topic discussed in the SOCR AP Curricumum should contain the following subsections:
- Motivation/Problem: A real data set and fundamental challenge.
- Approach: Models & strategies for solving the problem, data understanding & inference.
- Model Validation: Checking/affirming underlying assumptions.
- Computational Resources: Internet-based SOCR Tools (including offline resources, e.g., tables).
- Examples: computer simulations and real observed data.
- Hands-on activities: Step-by-step practice problems.
Introduction to Statistics
No mater how controlled the environment, the protocol or the design, virtually any repeated measurement, observation, experiment, trial, study or survey is bound to generate data that varies because of intrinsic (internal to the system) or extrinsic (due to the ambient environment) effects.
Uses and Abuses of Statistics
Design of Experiments
Statistics with Calculators and Computers
Describing, Exploring, and Comparing Data
Summarizing data with Frequency Tables
Pictures of Data
Measures of Central Tendency
Measures of Variation
Measures of Position
Exploratory Data Analysis
Probability
Fundamentals
Addition Rule
Multiplication Rule
Probabilities through Simulations
Counting
Probability Distributions
Random Variables
Bernoulli & Binomial Experiments
Geometric, HyperGeometric & Negative Binomial
Mean, Variance, and Standard Deviation for the Binomial Distribution
Poisson Distribution
Normal Probability Distributions
The Standard Normal Distribution
Nonstandard Normal Distribution: Finding Probabilities
Nonstandard Normal Distributions: Finding Scores
Relations Between Distributions
The Central Limit Theorem
Law of Large Numbers
Normal Distribution as Approximation to Binomial Distribution
Poisson Approximation to Binomial Distribution
Binomial Approximation to HyperGeometric
Normal Approximation to Poisson
Estimates and Sample Sizes
Estimating a Population Mean: Large Samples
Estimating a Population Mean: Small Samples
Estimating a Population Proportion
Estimating a Population Variance
Hypothesis Testing
Fundamentals of Hypothesis Testing
Testing a Claim about a Mean: Large Samples
Testing a Claim about a Mean: Small Samples
Testing a Claim about a Proportion
Testing a Claim about a Standard Deviation or Variance
Inferences from Two Samples
Inferences about Two Means: Dependent Samples
Inferences about Two Means: Independent and Large Samples
Comparing Two Variances
Inferences about Two Means: Independent and Small Samples
Inferences about Two Proportions
Correlation and Regression
Correlation
Regression
Variation and Prediction Intervals
Multiple Regression
Multinomial Experiments and Contingency Tables
Multinomial Experiments: Goodness-of-Fit
Contingency Tables: Independence and Homogeneity
Statistical Process Control
Control Charts for Variation and Mean
Control Charts for Attributes
