Part I Descriptive Statistics 
Unit 1 Statistics 3 
1．1 What is Statistics? 4 
1．1．1 Meanings of Statistics 4 
1．1．2 Definition of Statistics 5 
1．1．3 Types of Statistics 6 
1．1．4 Applications of Statistics 6 
1．2 The language of Statistics 9 
1．2．1 Population and Sample 9 
1．2．2 Kinds of Variables 11 
1．3 Measurability and Variability 14 
1．4 Data Collection 16 
1．4．1 The Data Collection Process 17 
1．4．2 Sampling Frame and Elements 18 
1．5* Single-Stage Methods 21 
1．5．1 Simple Random Sample 21 
1．5．2 Systematic Sample 22 
1．6* Multistage Methods 25 
1．7* Types of Statistical Study 27 
1．8 The Process of a Statistical Study 31 
Glossary 34 
Reading English Materials 35 
Passage 1． What is Statistics? 35 
Passage 2． From Data to Foresight 35 
Problems 36 
Unit 2 Descriptive Analysis of Single-Variable Data 40 
2．1 Graphs， Pareto Diagrams， and Stem-and-Leaf Displays 41 
2．1．1 Qualitative Data 41 
2．1．2 Quantitative Data 43 
2．2 Frequency Distributions and Histograms 47 
2．2．1 Frequency Distribution 47 
2．2．2 Histograms 51 
2．2．3 Cumulative Frequency Distribution and Ogives 53 
2．3 Measures of Central Tendency 55 
2．3．1 Finding the Mean 55 
2．3．2 Finding the Median 56 
2．3．3 Finding the Mode 57 
2．3．4 Finding the Midrange 58 
2．4 Measures of Dispersion 60 
2．4．1 Sample Standard Deviation 62 
2．5 Measures of Position 64 
2．5．1 Quartiles 64 
2．5．2 Percentiles 64 
2．5．3 Other Measures of Position 66 
2．6 Interpreting and Understanding Standard Deviation 70 
2．6．1 The Empirical Rule and Testing for Normality 70 
2．6．2 Chebyshev’s Theorem 72 
Glossary 74 
Problems 75 
Unit 3 Descriptive Analysis of Bivariate Data 79 
3．1 Bivariate Data 80 
3．1．1 Two Qualitative Variables 80 
3．1．2 One Qualitative and One Quantitative Variable 82 
3．1．3 Two Quantitative Variables 83 
3．2 Linear Correlation 85 
3．2．1 Calculating the Linear Correlation Coefficient， r 86 
*3．2．2 Causation and Lurking Variables 89 
3．3 Linear Regression 91 
3．3．1 Line of Best Fit 92 
3．3．2 Making Predictions 97 
Reading English Materials 99 
Passage 1． The First Regression 99 
Passage 2． Simpson’s Paradox 99 
Problems 100 
Unit 4 Introduction to Probability 104 
4．1 Sample Spaces， Events and Sets 105 
4．1．1 Introduction 105 
4．1．2 Sample Spaces 105 
4．1．3 Events 106 
4．1．4 Set Theory 108 
4．2 Probability Axioms and Simple Counting Problems 109 
4．2．1 Probability Axioms and Simple Properties 109 
4．2．2 Interpretations of Probability 111 
4．2．3 Classical Probability 112 
4．2．4 The Multiplication Principle 113 
4．3 Permutations and Combinations 115 
4．3．1 Introduction 115 
4．3．2 Permutations 116 
4．3．3 Combinations 118 
4．3．4 The Difference Between Permutations and Combinations 120 
4．4 Conditional Probability and the Multiplication Rule 122 
4．4．1 Conditional Probability 122 
4．4．2 The Multiplication Rule 123 
4．5 Independent Events， Partitions and Bayes Theorem 124 
4．5．1 Independence 124 
4．5．2 Partitions 125 
4．5．3 Law of Total Probability 126 
4．5．4 Bayes Theorem 126 
4．5．5 Bayes Theorem for Partitions 127 
Reading English Materials 130 
Passage 1． Probability and Odds 130 
Passage 2． The Relationship between Odds and Probability 130 
Passage 3． How the Odds Change across the Range of the Probability 131 
Problems 132 
Unit 5 Discrete Probability Models 134 
5．1 Introduction， Mass Functions and Distribution Functions 135 
5．1．1 Introduction 135 
5．1．2 Probability Mass Functions (PMFs) 136 
5．1．3 Cumulative Distribution Functions (CDFs) 137 
5．2 Expectation and Variance for Discrete Random Quantities 138 
5．2．1 Expectation 138 
5．2．2 Variance 139 
5．3 Properties of Expectation and Variance 140 
5．3．1 Expectation of a Function of a Random Quantity 140 
5．3．2 Expectation of a Linear Transformation 140 
5．3．3 Expectation of the Sum of Two Random Quantities 141 
5．3．4 Expectation of an Independent Product 141 
5．3．5 Variance of an Independent Sum 142 
5．4 The Binomial Distribution 142 
5．4．1 Introduction 142 
5．4．2 Bernoulli Random Quantities 143 
5．4．3 The Binomial Distribution 143 
5．4．4 Expectation and Variance of a Binomial Random Quantity 145 
5．5 The Geometric Distribution 146 
5．5．1 PMF 146 
5．5．2 CDF 147 
5．5．3 Useful Series in Probability 148 
5．5．4 Expectation and Variance of Geometric Random Quantities 148 
5．6 The Poisson Distribution 149 
5．6．1 Poisson as the Limit of a Binomial 149 
5．6．2 PMF 150 
5．6．3 Expectation and Variance of Poisson 151 
5．6．4 Sum of Poisson Random Quantities 152 
5．6．5 The Poisson Process 152 
Reading English Materials 154 
Passage 1． The Founder of Modern Statistics―Karl Pearson 154 
Passage 2． The Relations of Several Discrete Probability Models 154 
Problems 155 
Unit 6 Discrete Probability Models 158 
6．1 Introduction， PDF and CDF 159 
6．1．1 Introduction 159 
6．1．2 The Probability Density Function 159 
6．1．3 The Distribution Function 160 
6．1．4 Median and Quartiles 161 
6．2 Properties of Continuous Random Quantities 161 
6．2．1 Expectation and variance of continuous random quantities 161 
6．2．2 PDF and CDF of a Linear Transformation 162 
6．3 The Uniform Distribution 163 
6．4 The Exponential Distribution 165 
6．4．1 Definition and Properties 165 
6．4．2 Relationship with the Poisson Process 166 
6．4．3 The Memoryless Property 167 
6．5 The Normal Distribution 168 
6．5．1 Definition 168 
6．5．2 Properties 168 
6．6 The Standard Normal Distribution 169 
6．6．1 Properties of the Standard Normal Distribution 170 
6．6．2 Finding Area to The Right of z = 0 171 
6．6．3 Finding Area in The Right Tail of a Normal Curve 171 
6．6．4 Finding Area to the Left of a Positive z Value 172 
6．6．5 Finding Area from a Negative z to z = 0 172 
6．6．6 Finding Area in the Left Tail of a Normal Curve 172 
6．6．7 Finding Area from A Negative z to a Positive z 172 
6．6．8 Finding Area Between two z Values of the Same Sign 173 
6．6．9 Finding z-Scores Associated with a Percentile 173 
6．6．10 Finding z-scores that Bound an Area 174 
6．7 Applications of Normal Distributions 175 
6．7．1 Probabilities and Normal Curves 175 
6．7．2 Using the Normal Curve and z 176 
6．8 Specific z-score 178 
6．8．1 Visual Interpretation of z(a) 179 
6．8．2 Determining Corresponding z Values for z (a) 179 
6．8．3 Determining z-scores for Bounded Areas 180 
6．9 Normal Approximation of Binomial and Poisson 181 
6．9．1 Normal Approximation of the Binomial 181 
6．9．2 Normal Approximation of the Poisson 182 
Problems 182 
Unit 7 Sampling Distributions and CLT 187 
7．1 Sampling Distributions 188 
7．1．1 Forming a Sampling Distribution of Means 188 
7．1．2 Creating a Sampling Distribution of Sample Means 189 
7．2 The Sampling Distribution of Sample Means 192 
7．2．1 Central Limit Theorem 193 
7．2．2 Constructing a Sampling Distribution of Sample Means 194 
7．3 Application of the Sampling Distribution of Sample Means 199 
7．3．1 Converting Information into z-scores 199 
7．3．2 Distribution of and Increasing Individual Sample Size 200 
7．4 Advanced Central Limit Theorem 202 
7．4．1 Central Limit Theorem (Sample Mean) 203 
7．4．2 Central Limit Theorem (Sample Sum) 203 
Problems 207 
Part II Inferential Statistics 
Unit 8 Introduction to Statistical Inferences 210 
8．1 Point Estimation and Interval Estimation 211 
8．1．1 Point Estimate 211 
8．1．2 Interval Estimate 212 
8．2 Estimation of Mean m (s Known) 214 
8．2．1 The Principle of Constructing a Confidence Interval 214 
8．2．2 Applications 216 
8．2．3 Sample Size and Confidence Interval 217 
8．3 Introduction to Hypothesis Testing 220 
8．3．1 Null Hypothesis and Alternative Hypothesis 220 
8．3．2 Four Possible Outcomes in a Hypothesis Test 222 
8．4 Formulating the Statistical Null and Alternative Hypotheses 226 
8．4．1 Writing Null and Alternative Hypothesis in One-Tailed Situation 226 
8．4．2 Writing Null and Alternative Hypothesis in Two-Tailed Situation 227 
8．5 Hypothesis Test of Mean m (s Known)： A Probability-Value Approach 228 
8．5．1 One-Tailed Hypothesis Test Using the p-Value Approach 229 
8．5．2 Two-Tailed Hypothesis Test Using the p-Value Approach 233 
8．5．3 Evaluating the p-Value Approach 234 
8．6 Hypothesis Test of Mean m (s Known)： A Classical Approach 235 
8．6．1 One-Tailed Hypothesis Test Using the Classical Approach 236 
8．6．2 Two-Tailed Hypothesis Test Using the Classical Approach 239 
Problems 241 
Unit 9 Inferences Involving One Population 246 
9．1 Inferences about the Mean m (s Unknown) 247 
9．1．1 Using the t-Distribution Table 249 
9．1．2 Confidence Interval Procedure 251 
9．1．3 Hypothesis-Testing Procedure 252 
9．2 Inferences about the Binomial Probability of Success 258 
9．2．1 Confidence Interval Procedure 259 
9．2．2 Determining Sample Size 261 
9．2．3 Hypothesis-Testing Procedure 263 
9．3 Inferences about the Variance and Standard Deviation 268 
9．3．1 Critical Values of Chi-Square 269 
9．3．2 Hypothesis-Testing Procedure 270 
Problems 279 
Unit 10 Inferences Involving Two Populations 284 
10．1 Dependent and Independent Samples 285 
10．2 Inferences Concerning the Mean Difference Using Two Dependent Samples 287 
10．2．1 Procedures and Assumptions for Inferences Involving Paired Data 287 
10．2．2 Confidence Interval Procedure 288 
10．2．3 Hypothesis-Testing Procedure 290 
10．3 Inferences Concerning the Difference between Means Using Two Independent 
Samples 294 
10．3．1 Confidence Interval Procedure 295 
10．3．2 Hypothesis-Testing Procedure 297 
10．4 Inferences Concerning the Difference between Proportions 301 
10．4．1 Confidence Interval Procedure 303 
10．4．2 Hypothesis-Testing Procedure 304 
10．5 Inferences Concerning the Ratio of Variances Using Two Independent Samples 308 
10．5．1 Writing for the Equality of Variances 308 
10．5．2 Using the F-Distribution 309 
10．5．3 One-Tailed Hypothesis Test for the Equality of Variances 310 
10．5．4 Critical F-Values for One- and Two-Tailed Tests 313 
Problems 315 
Unit 11 An Introduction to Simple Regression 321 
11．1 Regression as a Best Fitting Line 322 
11．1．1 Regression as a Best Fitting Line 322 
11．1．2 Errors and Residuals 324 
11．2 Interpreting OLS Estimates 326 
11．3 Fitted Values and R2： Measuring the Fit of a Regression Model 328 
11．4 Nonlinearity in Regression 331 
Reading English Materials 335 
Problems 336 
Part III Statistical Methods and Data Science 
Unit 12 Statistics and Data Science 339 
12．1 Statistics and Data Science (I) 340 
12．1．1 What is Data Science 340 
12．1．2 Statistics and Data Science 340 
12．2 Statistics and Data Science (II) 343 
12．2．1 Statistics as Part of Data Science 343 
12．2．2 The Modern Statistical Analysis Process 344 
12．2．3 Statistician and Data Scientist 345 
12．3 Statistical Thinking 348 
12．3．1 What is Statistical Thinking 348 
12．3．2 The Two Cultures of Statistical Modeling 348 
12．3．3 A New Research Community 350 
12．4 Distinguishing Analytics， Business Intelligence， Data Science 352 
12．4．1 Analytics 352 
12．4．2 Business Intelligence 355 
12．4．3 Data Science 356 
Reading English Materials 359 
Problems 361 
Commonly Used Statistical Terms 362 
Appendix A Commonly Used Statistical Tables 367 
Appendix B Summary of Univariate Descriptive Statistics and Graphs for the Four 
Level of Measurement 379 
Appendix C Order of Magnitude of Data 380 
References 381