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TABLE OF CONTENTS; PREFACE; CHAPTER 1: EDUCATIONAL PRINCIPLES FOR STATISTICS AND PROBABILITY; 1.1. INTRODUCTION; 1.2. FUNDAMENTAL IDEAS IN STATISTICS AND PROBABILITY; 1.2.1. Exploratory Data Analysis (Chapter 2); 1.2.2. Modelling Information by Probabilities (Chapter 3); 1.2.3. Exploring and Modelling Association (Chapter 4); 1.2.4. Sampling and Inference (Chapter 5); 1.3. COMPLEMENTARY VIEWS OF STATISTICS AND MATHEMATICS; 1.4. THE ROLE OF TECHNOLOGY; 1.5. ADAPTING THE LEVELS OF FORMALISATION TO THE DIVERSITY OF STUDENTS; 1.6. STATISTICAL AND PROBABILISTIC LITERACY
1.6.1. Statistical Literacy1.6.2. Statistical Literacy Components; 1.6.3. Actions and Resources Directed to Increase Statistical Literacy; 1.7. STATISTICAL AND PROBABILISTIC THINKING; 1.7.1. Statistical Thinking; 1.7.2. The Statistical Investigation Cycle; 1.7.3. Fundamental Types of Statistical Thinking; 1.7.4. Components of Probabilistic Thinking; 1.8. MAKING SENSE OF STATISTICS AND PROBABILITY; 1.9. STATISTICAL INVESTIGATIONS AND EXPERIMENTS; 1.10. FINAL THOUGHTS; CHAPTER 2: EXPLORATORY DATA ANALYSIS; 2.1. INTRODUCTION
2.2. A TEACHING SITUATION TO INTRODUCE ELEMENTARY STATISTICAL CONCEPTS AND PROCEDURES2.2.1. Starting Questions; 2.2.2. Exploring Qualitative Variables; 2.2.3. Exploring Numerical Variables; 2.2.4. Comparing Groups; 2.3. ADDITIONAL ACTIVITIES; 2.3.1. Exploring Continuous Variables; 2.3.2. Exploring Bivariate Relationships; 2.4. SYNTHESIS OF LEARNING GOALS; 2.4.1. Distribution and Different Types of Frequencies; 2.4.2. Simple Univariate Graphs; 2.4.3. Simple Summary Statistics; 2.4.4. Spirit of Exploratory Data Analysis (EDA); 2.4.5. Basic Strategies in Data Exploration
2.5. STUDENTS' REASONING AND POTENTIAL DIFFICULTIES2.5.1. Graphical Competencies and Communication Skills; 2.5.2. Errors in Producing Graphs; 2.5.3. Understanding Measures of Central Tendency or Centre; 2.5.4. Understanding Spread; 2.5.5. Understanding Order Statistics; 2.6. ADDITIONAL RESOURCES; 2.6.1. Journals and Books; 2.6.2. Data Sets; 2.6.3. Internet Resources; APPENDIX: DATA; CHAPTER 3: MODELLING INFORMATION BY PROBABILITIES; 3.1. INTRODUCTION; 3.2. TEACHING SITUATIONS TO CHARACTERISE PROBABILITY; 3.2.1. Frequentist Probability: Investigating Coin Tossing
3.2.2. Subjectivist Probability: The Insurance Contract3.2.3. Laplace (A Priori) Probability: Calibrating Weights of Evidence; 3.3. TEACHING SITUATIONS INTRODUCING CONDITIONAL PROBABILITY; 3.3.1. Conditional Probability and Circumstantial Evidence; 3.3.2. Conditional Probability and Compound Probability; 3.4. ADDITIONAL TEACHING ACTIVITIES; 3.4.1. Random Variables; 3.4.2. Additivity of Expected Value and Variance for Repeated Experiments; 3.4.3. Distribution Models for Standard Situations; 3.4.4. Central theorems; Central Limit Theorem; 3.5. SYNTHESIS OF LEARNING GOALS
1.6.1. Statistical Literacy1.6.2. Statistical Literacy Components; 1.6.3. Actions and Resources Directed to Increase Statistical Literacy; 1.7. STATISTICAL AND PROBABILISTIC THINKING; 1.7.1. Statistical Thinking; 1.7.2. The Statistical Investigation Cycle; 1.7.3. Fundamental Types of Statistical Thinking; 1.7.4. Components of Probabilistic Thinking; 1.8. MAKING SENSE OF STATISTICS AND PROBABILITY; 1.9. STATISTICAL INVESTIGATIONS AND EXPERIMENTS; 1.10. FINAL THOUGHTS; CHAPTER 2: EXPLORATORY DATA ANALYSIS; 2.1. INTRODUCTION
2.2. A TEACHING SITUATION TO INTRODUCE ELEMENTARY STATISTICAL CONCEPTS AND PROCEDURES2.2.1. Starting Questions; 2.2.2. Exploring Qualitative Variables; 2.2.3. Exploring Numerical Variables; 2.2.4. Comparing Groups; 2.3. ADDITIONAL ACTIVITIES; 2.3.1. Exploring Continuous Variables; 2.3.2. Exploring Bivariate Relationships; 2.4. SYNTHESIS OF LEARNING GOALS; 2.4.1. Distribution and Different Types of Frequencies; 2.4.2. Simple Univariate Graphs; 2.4.3. Simple Summary Statistics; 2.4.4. Spirit of Exploratory Data Analysis (EDA); 2.4.5. Basic Strategies in Data Exploration
2.5. STUDENTS' REASONING AND POTENTIAL DIFFICULTIES2.5.1. Graphical Competencies and Communication Skills; 2.5.2. Errors in Producing Graphs; 2.5.3. Understanding Measures of Central Tendency or Centre; 2.5.4. Understanding Spread; 2.5.5. Understanding Order Statistics; 2.6. ADDITIONAL RESOURCES; 2.6.1. Journals and Books; 2.6.2. Data Sets; 2.6.3. Internet Resources; APPENDIX: DATA; CHAPTER 3: MODELLING INFORMATION BY PROBABILITIES; 3.1. INTRODUCTION; 3.2. TEACHING SITUATIONS TO CHARACTERISE PROBABILITY; 3.2.1. Frequentist Probability: Investigating Coin Tossing
3.2.2. Subjectivist Probability: The Insurance Contract3.2.3. Laplace (A Priori) Probability: Calibrating Weights of Evidence; 3.3. TEACHING SITUATIONS INTRODUCING CONDITIONAL PROBABILITY; 3.3.1. Conditional Probability and Circumstantial Evidence; 3.3.2. Conditional Probability and Compound Probability; 3.4. ADDITIONAL TEACHING ACTIVITIES; 3.4.1. Random Variables; 3.4.2. Additivity of Expected Value and Variance for Repeated Experiments; 3.4.3. Distribution Models for Standard Situations; 3.4.4. Central theorems; Central Limit Theorem; 3.5. SYNTHESIS OF LEARNING GOALS