Advanced Statistics and Probability

          Module 1: Introduction to Statistics and Probability

Section 1: Understanding Data and Variables  
- Lesson 1: Defining Data and Its Role  
  Module 1, Section 1, Lesson 1: An introduction to what data is and why it matters  
- Lesson 2: Types of Data – Quantitative vs. Qualitative  
  Module 1, Section 1, Lesson 2: Exploring different kinds of data and their characteristics  

Section 2: Data Collection and Ethics  
- Lesson 1: Methods of Data Collection  
  Module 1, Section 2, Lesson 1: Overview of surveys, experiments, and observational studies  
- Lesson 2: Ethical Considerations in Data Gathering  
  Module 1, Section 2, Lesson 2: Understanding privacy, consent, and responsible data use  

Section 3: Introduction to Statistical Terminology  
- Lesson 1: Key Terms in Statistics  
  Module 1, Section 3, Lesson 1: Defining mean, median, mode, and range in everyday language  
- Lesson 2: Understanding Variables and Parameters  
  Module 1, Section 3, Lesson 2: Differentiating between variables and parameters with simple examples  

Section 4: Visual Representation of Data  
- Lesson 1: Basic Graphs and Charts  
  Module 1, Section 4, Lesson 1: Learning about bar graphs, pie charts, and line graphs  
- Lesson 2: Interpreting Visual Data  
  Module 1, Section 4, Lesson 2: Tips for reading and understanding graphical representations  

Section 5: Basic Concepts in Probability  
- Lesson 1: Introduction to Probability Concepts  
  Module 1, Section 5, Lesson 1: The fundamentals of chance and uncertainty  
- Lesson 2: Simple Experiments in Probability  
  Module 1, Section 5, Lesson 2: Conducting basic probability experiments like coin flips and dice rolls  

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Module 2: Descriptive Statistics Fundamentals

Section 1: Measures of Central Tendency  
- Lesson 1: Exploring the Mean  
  Module 2, Section 1, Lesson 1: Calculating and interpreting the average of a data set  
- Lesson 2: Understanding Median and Mode  
  Module 2, Section 1, Lesson 2: Finding and using the median and mode in simple datasets  

Section 2: Measures of Dispersion  
- Lesson 1: Range and Variability  
  Module 2, Section 2, Lesson 1: Learning how range describes data spread  
- Lesson 2: Introduction to Variance and Standard Deviation  
  Module 2, Section 2, Lesson 2: Understanding how these measures indicate data dispersion  

Section 3: Organizing Data  
- Lesson 1: Frequency Tables  
  Module 2, Section 3, Lesson 1: How to build and interpret frequency distributions  
- Lesson 2: Grouped Data and Histograms  
  Module 2, Section 3, Lesson 2: Visualizing data using grouped formats and histograms  

Section 4: Percentages and Proportions  
- Lesson 1: Calculating Percentages  
  Module 2, Section 4, Lesson 1: Learning percentage calculations from raw numbers  
- Lesson 2: Working with Proportions  
  Module 2, Section 4, Lesson 2: Understanding how parts relate to a whole in datasets  

Section 5: Summarizing Data  
- Lesson 1: Creating Summaries from Data Sets  
  Module 2, Section 5, Lesson 1: Techniques for summarizing data effectively  
- Lesson 2: Using Summary Statistics in Everyday Situations  
  Module 2, Section 5, Lesson 2: Applying summary statistics to interpret real data  

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Module 3: Probability Essentials

Section 1: Basic Concepts of Probability  
- Lesson 1: Defining Probability  
  Module 3, Section 1, Lesson 1: Understanding probability as a measure of chance  
- Lesson 2: Simple Probability Calculations  
  Module 3, Section 1, Lesson 2: Performing basic probability operations with simple examples  

Section 2: Experimental and Theoretical Probability  
- Lesson 1: Theoretical Probability Concepts  
  Module 3, Section 2, Lesson 1: Differentiating theoretical ideas from experimental observations  
- Lesson 2: Conducting Simple Probability Experiments  
  Module 3, Section 2, Lesson 2: Gathering data from experiments to compare with theory  

Section 3: Independent and Dependent Events  
- Lesson 1: Understanding Independent Events  
  Module 3, Section 3, Lesson 1: What makes events independent and how to calculate their probabilities  
- Lesson 2: Introduction to Dependent Events  
  Module 3, Section 3, Lesson 2: Exploring events that influence one another and calculating their outcomes  

Section 4: Compound Events  
- Lesson 1: Combining Probabilities  
  Module 3, Section 4, Lesson 1: Learning how to deal with two or more events at once  
- Lesson 2: Real-Life Examples of Compound Events  
  Module 3, Section 4, Lesson 2: Applying compound event concepts with everyday scenarios  

Section 5: Applications of Basic Probability  
- Lesson 1: Using Probability in Games and Sports  
  Module 3, Section 5, Lesson 1: Practical examples to understand probability in fun contexts  
- Lesson 2: Everyday Decision Making with Probability  
  Module 3, Section 5, Lesson 2: Exploring how probability informs choices and risk management  

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Module 4: Basics of Inferential Statistics

Section 1: Sampling Methods  
- Lesson 1: Introduction to Sampling  
  Module 4, Section 1, Lesson 1: Understanding why and how sampling is used in statistics  
- Lesson 2: Common Sampling Techniques  
  Module 4, Section 1, Lesson 2: Overview of random, stratified, and systematic sampling  

Section 2: Confidence Intervals  
- Lesson 1: What Is a Confidence Interval?  
  Module 4, Section 2, Lesson 1: Explaining the concept of estimation and margin of error  
- Lesson 2: Calculating Basic Confidence Intervals  
  Module 4, Section 2, Lesson 2: Simple methods to estimate confidence intervals for data  

Section 3: Hypothesis Testing Fundamentals  
- Lesson 1: Steps in Hypothesis Testing  
  Module 4, Section 3, Lesson 1: Introducing null and alternative hypotheses with simple examples  
- Lesson 2: Understanding Errors and Significance  
  Module 4, Section 3, Lesson 2: Exploring Type I and Type II errors and what significance means  

Section 4: Using P-Values  
- Lesson 1: Definition and Role of P-Values  
  Module 4, Section 4, Lesson 1: What p-values indicate in hypothesis testing  
- Lesson 2: Interpreting P-Values in Simple Studies  
  Module 4, Section 4, Lesson 2: Learning to draw conclusions based on p-value results  

Section 5: Practical Experimentation in Inference  
- Lesson 1: Designing a Simple Statistical Experiment  
  Module 4, Section 5, Lesson 1: Laying out the steps for a basic inferential study  
- Lesson 2: Analyzing Experiment Results  
  Module 4, Section 5, Lesson 2: Simple data interpretation techniques that lead to statistical inferences  

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Module 5: Real-World Data Analysis and Applications

Section 1: Introduction to Data Analysis Tools  
- Lesson 1: Overview of Data Analysis Software  
  Module 5, Section 1, Lesson 1: Familiarization with spreadsheets and simple statistical tools  
- Lesson 2: Collecting Data from Real-World Sources  
  Module 5, Section 1, Lesson 2: How to find and prepare real data for analysis  

Section 2: Interpreting Real-World Datasets  
- Lesson 1: Reading Data from Graphs and Tables  
  Module 5, Section 2, Lesson 1: Techniques for extracting information from common data presentations  
- Lesson 2: Identifying Trends and Patterns  
  Module 5, Section 2, Lesson 2: Learning strategies to notice trends in everyday data  

Section 3: Real-Life Applications of Descriptive Statistics  
- Lesson 1: Analyzing School and Community Data  
  Module 5, Section 3, Lesson 1: Practical examples using familiar contexts  
- Lesson 2: Summarizing and Communicating Findings  
  Module 5, Section 3, Lesson 2: How to prepare and present statistical summaries  

Section 4: Basic Business and Economics Applications  
- Lesson 1: Introduction to Market Statistics  
  Module 5, Section 4, Lesson 1: Using statistics to understand market and consumer data  
- Lesson 2: Applying Statistical Analysis in Everyday Economics  
  Module 5, Section 4, Lesson 2: Real-world scenarios demonstrating economic data analysis  

Section 5: Bringing It All Together  
- Lesson 1: Case Study: A Simple Data Analysis Project  
  Module 5, Section 5, Lesson 1: Walkthrough of a basic project using collected data  
- Lesson 2: Reflecting on Findings and Future Applications  
  Module 5, Section 5, Lesson 2: Discussion of the importance of statistical literacy and next steps in learning