Part Ⅰ Descriptive Statistics

Unit 1 Statistics

1.1 What is Statistics？

1.1.1 Meanings of Statistics

1.1.2 Definition of Statistics

1.1.3 Types of Statistics

1.1.4 Applications of Statistics

1.2 The language of Statistics

1.2.1 Population and Sample

1.2.2 Kinds of Variables

1.3 Measurability and Variability

1.4 Data Collection

1.4.1 The Data Collection Process

1.4.2 Sampling Frame and Elements

1.5 Single-Stage Methods

1.5.1 Simple Random Sample

1.5.2 Systematic Sample

1.6 Multistage Methods

1.7 Types of Statistical Study

1.8 The Process of a Statistical Study

Glossary

Reading English Materials

Passage 1．What is Statistics？

Passage 2．From Data to Foresight

Problems

Unit 2 Descriptive Analysis of Single-Variable Data

2.1 Graphs，Pareto Diagrams，and Stem-and-Leaf Displays

2.1.1 Qualitative Data

2.1.2 Quantitative Data

2.2 Frequency Distributions and Histograms

2.2.1 Frequency Distribution

2.2.2 Histograms

2.2.3 Cumulative Frequency Distribution and Ogives

2.3 Measures of Central Tendency

2.3.1 Finding the Mean

2.3.2 Finding the Median

2.3.3 Finding the Mode

2.3.4 Finding the Midrange

2.4 Measures of Dispersion

2.4.1 Sample Standard Deviation

2.5 Measures of Position

2.5.1 Quartiles

2.5.2 Percentiles

2.5.3 Other Measures of Position

2.6 Interpreting and Understanding Standard Deviation

2.6.1 The Empirical Rule and Testing for Normality

2.6.2 Chebyshev's Theorem

Glossary

Problems

Unit 3 Descriptive Analysis of Bivariate Data

3.1 Bivariate Data

3.1.1 Two Qualitative Variables

3.1.2 One Qualitative and One Quantitative Variable

3.1.3 Two Quantitative Variables

3.2 Linear Correlation

3.2.1 Calculating the Linear Correlation Coefficient,r

3.2.2 Causation and Lurking Variables

3.3 Linear Regression

3.3.1 Line of Best Fit

3.3.2 Making Predictions

Reading English Materials

Passage 1．The First Regression

Passage 2．Simpson's Paradox

Problems

Unit 4 Introduction to Probability

4.1 Sample Spaces,Events and Sets

4.1.1 Introduction

4.1.2 Sample Spaces

4.1.3 Events

4.1.4 Set Theory

4.2 Probability Axioms and Simple Counting Problems

4.2.1 Probability Axioms and Simple Properties

4.2.2 Interpretations of Probability

4.2.3 Classical Probability

4.2.4 The Multiplication Principle

4.3 Permutations and Combinations

4.3.1 Introduction

4.3.2 Pemutations

4.3.3 Combinations

4.3.4 The Difference Between Permutations and Combinations

4.4 Conditional Probability and the Multiplication Rule

4.4.1 Conditional Probability

4.4.2 The Multiplication Rule

4.5 Independent Events，Partitions and Bayes Theorem

4.5.1 Independence

4.5.2 Partitions

4.5.3 Law of Total Probability

4.5.4 Bayes Theorem

4.5.5 Bayes Theorem for Partitions

Reading English Materials

Passage 1．Probability and Odds

Passage 2．The Relationship between Odds and Probability

Passage 3．How the Odds Change across the Range of the Probability

Problems

Unit 5 Discrete Probability Models

5.1 Introduction,Mass Functions and Distribution Functions

5.1.1 Introduction

5.1.2 Probability Mass Functions（PMFs）

5.1.3 Cumulative Distribution Functions（CDFs）

5.2 Expectation and Variance for Discrete Random Quantities

5.2.1 Expectation

5.2.2 Variance

5.3 Properties of Expectation and Variance

5.3.1 Expectation of a Function of a Random Quantity

5.3.2 Expectation of a Linear Transformation

5.3.3 Expectation of the Sum of Two Random Quantities

5.3.4 Expectation of an Independent Product

5.3.5 Variance of an Independent Sum

5.4 The Binomial Distribution

5.4.1 Introduction

5.4.2 Bemoulli Random Quantities

5.4.3 The Binomial Distribution

5.4.4 Expectation and Variance of a Binomial Random Quantity

5.5 The Geometric Distribution

5.5.1 PMF

5.5.2 CDF

5.5.3 Useful Series in Probability

5.5.4 Expectation and Variance of Geometric Random Quantities

5.6 The Poisson Distribution

5.6.1 Poisson as the Limit of a Binomial

5.6.2 PMF

5.6.3 Expectation and Variance of Poisson

5.6.4 Sum of Poisson Random Quantities

5.6.5 The Poisson Process

Reading English Materials

Passage 1．The Founder of Modern Statistics—Karl Pearson

Passage 2．The Relations of Several Discrete Probability Models

Problems

Unit 6 Discrete Probability Models

6.1 Introduction，PDF and CDF

6.1.1 Introduction

6.1.2 The Probability Density Function

6.1.3 The Distribution Function

6.1.4 Median and Quartiles

6.2 Properties of Continuous Random Quantities

6.2.1 Expectation and variance of continuous random quantities

6.2.2 PDF and CDF of a Linear Transformation

6.3 The Uniform Distribution

6.4 The Exponential Distribution

6.4.1 Definition and Properties

6.4.2 Relationship with the Poisson Process

6.4.3 The Memoryless Property

6.5 The Normal Distribution

6.5.1 Definition

6.5.2 Properties

6.6 The Standard Normal Distribution

6.6.1 Properties of the Standard Normal Distribution

6.6.2 Finding Area to The Right of z=0

6.6.3 Finding Areain The Right Tail of a Normal Curve

6.6.4 Finding Area to the Left of a Positive z Value

6.6.5 Finding Area from a Negative z to z=0

6.6.6 Finding Area in the Left Tail of a Normal Curve

6.6.7 Finding Area from A Negative z to a Positive z

6.6.8 Finding Area Between two z Values of the Same Sign

6.6.9 Finding z-Scores Associated with a Percentile

6.6.10 Finding z-scores that Bound an Area

6.7 Applications of Normal Distributions

6.7.1 Probabilities and Normal Curves

6.7.2 Using the Normal Curve and z

6.8 Specific z-score

6.8.1 Visual Interpretation of z（a）

6.8.2 Determining Corresponding z Values for z（a）

6.8.3 Determining z-scores for Bounded Areas

6.9 Normal Approximation of Binomial and Poisson

6.9.1 Normal Approximation of the Binomial

6.9.2 Normal Approximation of the Poisson

Problems

Unit 7 Sampling Distributions and CLT

7.1 Sampling Distributions

7.1.1 Forming a Sampling Distribution of Means

7.1.2 Creating a Sampling Distribution of Sample Means

7.2 The Sampling Distribution of Sample Means

7.2.1 Central Limit Theorem

7.2.2 Constructing a Sampling Distribution of Sample Means

7.3 Application of the Sampling Distribution of Sample Means

7.3.1 Converting？Information into z-scores

7.3.2 Distribution of？and Increasing Individual Sample Size

7.4 Advanced Central Limit Theorem

7.4.1 Central Limit Theorem（Sample Mean）

7.4.2 Central Limit Theorem（Sample Sum）

Problems

Part Ⅱ Inferential Statistics

Unit 8 Introduction to Statistical Inferences

8.1 Point Estimation and Interval Estimation

8.1.1 Point Estimate

8.1.2 Interval Estimate

8.2 Estimation of Meanμ（σKnown）

8.2.1 The Principle of Constructing a Confidence Interval

8.2.2 Applications

8.2.3 Sample Size and Confidence Interval

8.3 Introduction to Hypothesis Testing

8.3.1 Null Hypothesis and Alternative Hypothesis

8.3.2 Four Possible Outcomes in a Hypothesis Test

8.4 Formulating the Statistical Null and Alternative Hypotheses

8.4.1 Writing Null and Alternative Hypothesis in One-Tailed Situation

8.4.2 Writing Null and Alternative Hypothesis in Two-Tailed Situation

8.5 Hypothesis Test of Meanμ（σKnown）：A Probability-Value Approach

8.5.1 One-Tailed Hypothesis Test Using the p-Value Approach

8.5.2 Two-Tailed Hypothesis Test Using the p-Value Approach

8.5.3 Evaluating the p-Value Approach

8.6 Hypothesis Test of Meanμ（σKnown）：A Classical Approach

8.6.1 One-Tailed Hypothesis Test Using the Classical Approach

8.6.2 Two-Tailed Hypothesis Test Using the Classical Approach

Problems

Unit 9 Inferences Involving One Population

9.1 Inferences about the Meanμ（σUnknown）

9.1.1 Using the t-Distribution Table

9.1.2 Confidence Interval Procedure

9.1.3 Hypothesis-Testing Procedure

9.2 Inferences about the Binomial Probability of Success

9.2.1 Confidence Interval Procedure

9.2.2 Determining Sample Size

9.2.3 Hypothesis-Testing Procedure

9.3 Inferences about the Variance and Standard Deviation

9.3.1 Critical Values of Chi-Square

9.3.2 Hypothesis-Testing Procedure

Problems

Unit 10 Inferences Involving Two Populations

10.1 Dependent and Independent Samples

10.2 Inferences Concerning the Mean Difference Using Two Dependent Samples

10.2.1 Procedures and Assumptions for Inferences Involving Paired Data

10.2.2 Confidence Interval Procedure

10.2.3 Hypothesis-Testing Procedure

10.3 Inferences Conceming the Difference between Means Using Two Independent Samples

10.3.1 Confidence Interval Procedure

10.3.2 Hypothesis-Testing Procedure

10.4 Inferences Concerning the Difference between Proportions

10.4.1 Confidence Interval Procedure

10.4.2 Hypothesis-Testing Procedure

10.5 Inferences Concerning the Ratio ofVariances Using Two Independent Samples

10.5.1 Writing for the Equality of Variances

10.5.2 Using the F-Distribution

10.5.3 One-Tailed Hypothesis Test for the Equality of Variances

10.5.4 Critical F-Values for One-and Two-Tailed Tests

Problems

Unit 11 An Introduction to Simple Regression

11.1 Regression as a Best Fitting Line

11.1.1 Regression as a Best Fitting Line

11.1.2 Errors and Residuals

11.2 Interpreting OLS Estimates

11.3 Fitted Values and R2：Measuring the Fit of a Regression Model

11.4 Nonlinearity in Regression

Reading English Materials

Problems

Part Ⅲ Statistical Methods and Data Science

Unit 12 Statistics and Data Science

12.1 Statistics and Data Science（Ⅰ）

12.1.1 What is Data Science

12.1.2 Statistics and Data Science

12.2 Statistics and Data Science（Ⅱ）

12.2.1 Statistics as Part of Data Science

12.2.2 The Modern Statistical Analysis Process

12.2.3 Statistician and Data Scientist

12.3 Statistical Thinking

12.3.1 What is Statistical Thinking

12.3.2 The Two Cultures of Statistical Modeling

12.3.3 A New Research Community

12.4 Distinguishing Analytics，Business Intelligence，Data Science

12.4.1 Analytics

12.4.2 Business Intelligence

12.4.3 Data Science

Reading English Materials

Problems

Commonly Used Statistical Terms

Appendix A Commonly Used Statistical Tables

Appendix B Summary of Univariate Descriptive Statistics and Graphs for the Four Level of Measurement

Appendix C Order of Magnitude of Data

References