Quantitative Reasoning

Annotated Contents xi

Preface xvii

To the Student xxiii

To the Instructor xxv

Acknowledgments xxvii

Section I: Numerical Reasoning

Topic 1: Organizing Information Pictorially Using Charts and Graphs 2

Activity 1.1: World Motor Vehicle Production: Bar Graphs and Pie Charts 27

Activity 1.2: Medical Data and Class Data: Graphs with Excel 35

Activity 1.3: SATs and the Super Bowl: Creating and Interpreting Histograms 43

Topic 2: Bivariate Data 52

Activity 2.1: Estimating Dates: Scatterplots 69

Activity 2.2: State Governors’ Salaries and Per Capita Income: More on Scatterplots 75

Topic 3: Graphs of Functions 82

Activity 3.1: Temperature Patterns: Functions and Line Graphs 105

Activity 3.2: Rates of Change and Concavity 111

Topic 4: Multiple Variable Functions 118

Activity 4.1: Blood Alcohol Levels and Credit Cards: Working with More Than Two Variables 133

Topic 5: Proportional, Linear, and Piecewise Linear Functions 140

Activity 5.1: Rates of Change and Linear Functions 159

Topic 6: Modeling with Linear and Exponential Functions 166

Activity 6.1: The Genie’s Offer: Exponential Growth and Linear Growth 185

Activity 6.2: Lines of Best Fit 191

Topic 7: Logarithms and Scientific Notation 198

Activity 7.1: Richter Scale and Logarithms 213

Activity 7.2: Estimations, Scientifc Notation, and Properties of Logarithms 219

Topic 8: Indexes and Ratings 224

Activity 8.1: Measurement Difficulties and Indexes 243

Activity 8.2: Consumer Indexes 249

Topic 9: Personal Finances 256

Activity 9.1: Mortgages 277

Topic 10: Introduction to Problem Solving 284

Activity 10.1: Savings and Loans: Problem Solving and Using Scroll Bars 299

Activity 10.2: Asking and Answering a Research Question 305

Section II: Logical Reasoning

Topic 11: Decision Making 308

Activity 11.1: Ranking Cities: Ratings and Decisions 325

Topic 12: Inductive Reasoning 332

Activity 12.1: Analyzing Studies: Inductive Reasoning 345

Topic 13: Deductive Reasoning 354

Activity 13.1: Code-Breaking and Deductive Reasoning 375

Activity 13.2: Compound Statements Used in Reasoning 381

Activity 13.3: Quantified Statements and Deductive Reasoning: Direct and Indirect Reasoning 389

Topic 14: Apportionment 394

Activity 14.1: Methods of Apportionment: Quota Methods 409

Activity 14.2: Apportionment: Divisor Methods 415

Topic 15: More on Problem Solving 422

Activity 15.1: Making a Purchase Decision 433

Section III: Statistical Reasoning

Topic 16: Averages and Five-Number Summary 436

Activity 16.1: Visualizing Football Scores: Measures of Center and Spread 457

Topic 17: Standard Deviation, z-Score, and Normal Distributions 462

Activity 17.1: Coins, Presidents, and Justices: Normal Distributions and z-Scores 485

Topic 18: Basics of Probability 492

Activity 18.1: Simulations 511

Activity 18.2: Finding Probabilities 517

Topic 19: Conditional Probability and Tables 522

Activity 19.1: Diagnostic Testing and Conditional Probability 543

Topic 20: Sampling and Surveys 550

Activity 20.1: Sampling and Surveys 569

Topic 21: More on Decision Making 578

Activity 21.1: To Purchase a Warranty or Not: Making a Decision 593

Appendix

Excel Commands by Activity 597

Index 603