Quantitative Reasoning

Alicia Sevilla has a Ph.D. in mathematics from Cornell University and is Professor of Mathematics at Moravian College, where she has taught for over 20 years. She participated in the two FIPSE projects that produced the COMPANION TO CALCULUS and mentored other institutions to adopt the integrated approach. She recently served as Chair of the Department of Mathematics and Computer Science, and was co-director of a National Science Foundation grant to develop and implement a quantitative reasoning course. She is an active member of the Mathematical Association of America, and serves as Coordinat.

• Annotated Contents xiPreface xviiTo the Student xxiiiTo the Instructor xxvAcknowledgments xxviiSection I: Numerical ReasoningTopic 1: Organizing Information Pictorially Using Charts and Graphs 2Activity 1.1: World Motor Vehicle Production: Bar Graphs and Pie Charts 27Activity 1.2: Medical Data and Class Data: Graphs with Excel 35Activity 1.3: SATs and the Super Bowl: Creating and Interpreting Histograms 43Topic 2: Bivariate Data 52Activity 2.1: Estimating Dates: Scatterplots 69Activity 2.2: State Governors’ Salaries and Per Capita Income: More on Scatterplots 75Topic 3: Graphs of Functions 82Activity 3.1: Temperature Patterns: Functions and Line Graphs 105Activity 3.2: Rates of Change and Concavity 111Topic 4: Multiple Variable Functions 118Activity 4.1: Blood Alcohol Levels and Credit Cards: Working with More Than Two Variables 133Topic 5: Proportional, Linear, and Piecewise Linear Functions 140Activity 5.1: Rates of Change and Linear Functions 159Topic 6: Modeling with Linear and Exponential Functions 166Activity 6.1: The Genie’s Offer: Exponential Growth and Linear Growth 185Activity 6.2: Lines of Best Fit 191Topic 7: Logarithms and Scientific Notation 198Activity 7.1: Richter Scale and Logarithms 213Activity 7.2: Estimations, Scientifc Notation, and Properties of Logarithms 219Topic 8: Indexes and Ratings 224Activity 8.1: Measurement Difficulties and Indexes 243Activity 8.2: Consumer Indexes 249Topic 9: Personal Finances 256Activity 9.1: Mortgages 277Topic 10: Introduction to Problem Solving 284Activity 10.1: Savings and Loans: Problem Solving and Using Scroll Bars 299Activity 10.2: Asking and Answering a Research Question 305Section II: Logical ReasoningTopic 11: Decision Making 308Activity 11.1: Ranking Cities: Ratings and Decisions 325Topic 12: Inductive Reasoning 332Activity 12.1: Analyzing Studies: Inductive Reasoning 345Topic 13: Deductive Reasoning 354Activity 13.1: Code-Breaking and Deductive Reasoning 375Activity 13.2: Compound Statements Used in Reasoning 381Activity 13.3: Quantified Statements and Deductive Reasoning: Direct and Indirect Reasoning 389Topic 14: Apportionment 394Activity 14.1: Methods of Apportionment: Quota Methods 409Activity 14.2: Apportionment: Divisor Methods 415Topic 15: More on Problem Solving 422Activity 15.1: Making a Purchase Decision 433Section III: Statistical ReasoningTopic 16: Averages and Five-Number Summary 436Activity 16.1: Visualizing Football Scores: Measures of Center and Spread 457Topic 17: Standard Deviation, z-Score, and Normal Distributions 462Activity 17.1: Coins, Presidents, and Justices: Normal Distributions and z-Scores 485Topic 18: Basics of Probability 492Activity 18.1: Simulations 511Activity 18.2: Finding Probabilities 517Topic 19: Conditional Probability and Tables 522Activity 19.1: Diagnostic Testing and Conditional Probability 543Topic 20: Sampling and Surveys 550Activity 20.1: Sampling and Surveys 569Topic 21: More on Decision Making 578Activity 21.1: To Purchase a Warranty or Not: Making a Decision 593AppendixExcel Commands by Activity 597Index 603