Table of Contents
Introduction: Basic Ideas of Statistics
1 Data
Topics
-
What is Data?
Task: Identify Types of Statistics Task: Identify Data Types
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Where are the Data?
Tools:
Interactive Data Sets for Examining Maximum, Minimum and Range of Data Sets.
Interactive Data Sets for Examining Mean, Median and Mode of Data Sets. -
Presentation of Data and Histograms: Frequency, Relative Frequency, and Weights
Tools:
Build Histograms from Interactive Data Sets
Histograms from Frequency Information
Bins and Data Organization
Approximating Averages - Measure of Dispersion: How Spread is the Data?
- Other Descriptions of Data: Skewness, Kurtosis
Tasks
- Identify Types of Statistics
- Identify Data Types
- Find Maximum, Minimum and Range of Data Set
- Find Mean, Median and Mode of Data Set
- Build a Histogram
- Compute Relative Frequencies
- Approximate Mean from Relative Frequency Information
- Build a Histogram and Obtain Information about Data
- Determine Variance and Standard Deviation
- Approximate Standard Deviation from Frequency Data
- Determine Skewness and Kurtosis of a Data Set
Worksheets
Evaluation tools
2 Probability
Topics
-
Introductory Examples
Tools:
Interactive Model of Coin Flips
Interactive Model of Die Rolls
Interactive Model of Waiting Times - Axioms of Probability and Immediate Consequences
- Counting and More Examples
-
Some Basic Set Theory
Task: Using Venn Diagrams
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Conditional Probability, Bayes’ Theorem, and Independence
Task: Determine Conditional Probabilities Task: Use Bayes’ Theorem
- Random Variables
- Expected Value and Basic Properties
Task: Compute Expected Values- Moments and the Moment Generating Function
Task: Compute Moments- Chebyshevs’ Theorem
- Basic Models: Discrete Random Variables
Uniform
Bernoulli
Binomial
Geometric and Inverse Binomial
Poisson- Basic Models: Continuous Random Variables
Uniform
Exponential
NormalTasks
- Compute Probabilities of Simple Events
- Several Counting Problems
- Using Venn Diagrams
- Determine Conditional Probabilities
- Use Bayes’ Theorem
- Identify Random Variables
- Compute Expected Values
- Compute Moments
- Using Chebyshev’s Inequality
- Explore Binomial Densities
- Explore Geometric Densities
- Explore Poisson Densities
- Explore Rectangular Densities
- Explore Exponential Densities
- Explore Normal Densities
Evaluation Tools
- Compute Probabilities of Simple Events
- Several Counting Problems
- Using Venn Diagrams
- Determine Conditional Probabilities
- Use Bayes’ Theorem
- Identify Random Variables
- Compute Expected Values
- Compute Moments
- Using Chebyshev’s Inequality
- Basic Models â Discrete Random Variables
- Basic Models â Continuous Random Variables
3 Sampling
Topics
- The Idea – Understanding Underlying Probability
- Collection and Sample Bias
- Estimation
- Joint Density Functions and Independent Random Variables
- Further Properties of Expectation and Moment Generating Functions
- The Law of Large Numbers and Convergence to Probability
- Distribution of the Mean from a Normal Distribution
- Distribution of the Mean from a Non-normal Distribution
Tasks
Evaluation Tools
4 Interpretation and Inference – Drawing Conclusions
Topics
- Using Statistics – Analyzing Data through Understanding Underlying Probability
- Hypotheses, Hypothesis Testing, and Error
- Confidence Intervals for Normal Variables
- Distribution of Averages for Normal Variables
- Estimating the Mean of a Normal Variable from a Sample
- Sums of Chi-square Variables and Approximation of Variance
- Estimating Means and Variances in General
- Small Sample Sizes
- Hypothesis Testing Using Confidence Intervals
Tasks
- Accepting/Rejecting Hypotheses
- Confidence Intervals for a Normal Random Variable
- Confidence Intervals for the Average of a Sample of a Normal Random Variable
- Controlling Confidence Intervals with Sample Size
- Find Confidence Intervals for Proportions
- Estimate the Difference of the Means of Two Normal Random Variables
- Estimate the Difference of Two Proportions
Evaluation Tools
- Accepting/Rejecting Hypotheses
- Confidence Intervals for a Normal Random Variable
- Confidence Intervals for the Average of a Sample of a Normal Random Variable
- Controlling Confidence Intervals with Sample Size
- Find Confidence Intervals for Proportions
- Estimate the Difference of the Means of Two Normal Random Variables
- Estimate the Difference of Two Proportions
5 Correlation and Regression
Topics
6 Advanced Topics
Topics