S&DS 1000
Introductory Statistics
Complete Study Guide — All 13 Chapters
Independent Study Resource
Not affiliated with or endorsed by Yale University
Based on OpenStax Introductory Statistics (CC BY 4.0)
Licensed CC BY 4.0 — commercially sellable
Edition 2026
,Table of Contents
1. Sampling and Data
2. Descriptive Statistics
3. Probability Topics
4. Discrete Random Variables
5. Continuous Random Variables
6. The Normal Distribution
7. The Central Limit Theorem
8. Confidence Intervals
9. Hypothesis Testing with One Sample
10. Hypothesis Testing with Two Samples
11. The Chi-Square Distribution
12. Linear Regression and Correlation
13. F Distribution and One-Way ANOVA
14. Glossary of Key Terms
15. Formula Sheet
16. Final Exam Strategy and Study Checklist
17. References and Attribution
, Chapter 1 — Sampling and Data
Learning Objectives
1. Define key statistical terms: population, sample, parameter, statistic, variable, data.
2. Distinguish between descriptive and inferential statistics.
3. Identify types of sampling methods and their biases.
4. Describe experimental design principles and ethical considerations.
Key Definitions
Term Definition
Population The entire group of individuals or items under study.
Sample A subset of the population selected for study.
Parameter A numerical summary of a population (e.g., population mean μ).
Statistic A numerical summary of a sample (e.g., sample mean x̄ ).
Variable A characteristic that can take different values for different individuals.
Quantitative Variable A variable measured on a numerical scale.
Qualitative Variable A variable describing a category or quality.
Discrete Variable A quantitative variable with countable values.
Continuous Variable A quantitative variable with uncountable values in an interval.
Descriptive Statistics Organizing, summarizing, and presenting data.
Inferential Statistics Drawing conclusions about a population from a sample.
1.1 Populations and Samples
Statistical reasoning begins with a question about a population. Because studying an entire
population is often impractical, we study a sample and use inferential statistics to generalize.
The accuracy of inference depends on how well the sample represents the population.
Introductory Statistics
Complete Study Guide — All 13 Chapters
Independent Study Resource
Not affiliated with or endorsed by Yale University
Based on OpenStax Introductory Statistics (CC BY 4.0)
Licensed CC BY 4.0 — commercially sellable
Edition 2026
,Table of Contents
1. Sampling and Data
2. Descriptive Statistics
3. Probability Topics
4. Discrete Random Variables
5. Continuous Random Variables
6. The Normal Distribution
7. The Central Limit Theorem
8. Confidence Intervals
9. Hypothesis Testing with One Sample
10. Hypothesis Testing with Two Samples
11. The Chi-Square Distribution
12. Linear Regression and Correlation
13. F Distribution and One-Way ANOVA
14. Glossary of Key Terms
15. Formula Sheet
16. Final Exam Strategy and Study Checklist
17. References and Attribution
, Chapter 1 — Sampling and Data
Learning Objectives
1. Define key statistical terms: population, sample, parameter, statistic, variable, data.
2. Distinguish between descriptive and inferential statistics.
3. Identify types of sampling methods and their biases.
4. Describe experimental design principles and ethical considerations.
Key Definitions
Term Definition
Population The entire group of individuals or items under study.
Sample A subset of the population selected for study.
Parameter A numerical summary of a population (e.g., population mean μ).
Statistic A numerical summary of a sample (e.g., sample mean x̄ ).
Variable A characteristic that can take different values for different individuals.
Quantitative Variable A variable measured on a numerical scale.
Qualitative Variable A variable describing a category or quality.
Discrete Variable A quantitative variable with countable values.
Continuous Variable A quantitative variable with uncountable values in an interval.
Descriptive Statistics Organizing, summarizing, and presenting data.
Inferential Statistics Drawing conclusions about a population from a sample.
1.1 Populations and Samples
Statistical reasoning begins with a question about a population. Because studying an entire
population is often impractical, we study a sample and use inferential statistics to generalize.
The accuracy of inference depends on how well the sample represents the population.
