| Unit 1. Quantifying the World. Students learn the importance of data and how to locate
data in real world situations. | ||
| Chapter | Content | Memo Regarding |
| 1. Problem Solving | Framing a problem in terms of data | Performing the up-front analysis in response to a RFP from Carnivorous Cruise Lines concerning lack of attendance at its entertainment venues (No data file) |
| 2. Understanding the Role of Data | Collecting and organizing data to support problem solving | Creating data collection forms and displaying sample test data in spreadsheets for the Carnivorous Cruise Lines RFP (Create your own data file) |
| 3. Using Models to Interpret Data | Building simple models to analyze data using the mean, standard deviation and pivot tables | Analyzing sample data from Carnivorous Cruise Lines to make changes in the entertainment schedule (Data file) |
| Unit 2. Analyzing Data Through Spatial Models. Students learn how to use basic charts
and graphs to deeply understand a problem situation.
| ||
| Chapter | Content | Memo Regarding |
| 4. Box-and-Whisker Plots | Using boxplots and associated measures to build and analyze spatial models of data | Using boxplots to explore the salary structures of four different companies for two quite different managers in need of a job (Data file) |
| 5. Histograms | Using z-scores and histograms for understanding different distributions of data | Analyzing customer wait times at a fast food restaurant in response to customer complaints of poor service (Data file) |
| 6. Interpreting Spatial Models | Estimating statistics from summary data and connect the different spatial models (boxplots and histograms) to build a more complete understanding of a set of data | Analyzing ten different stocks in order to build financial portfolios for two quite different clients. (Data file) |
| Unit 3. Analyzing Data Through Linear Models. Students learn how to apply proportional
reasoning to understand data with one or more independent variables.
| ||
| Chapter | Content | Memo Regarding |
| 7. Correlation | Picturing and quantifying the relationship between two variables using correlation and trendlines | Using and interpreting trendlines to determine how in-city and out-of-city driving conditions effect maintenance costs for a trucking fleet (Data file) |
| 8. Simple Regression | Using simple linear regression to measure the effect of one variable upon another and to interpret how well our models fit the data | Building and interpreting simple regression models regarding the how various variables affect ridership on a commuter rail system (Data file) |
| 9. Multiple and Categorical Regression | Extending regression modeling into many dimensions and using qualitative variables | Building successive multivariable models using quantitative and qualitative variables to analyze how gender might be implicated in the salary structure at a company (Data file) |
| 10. Is the Model Any Good? | Exploring the reliability of linear models and introducing interaction terms into the models | Developing more realistic models of the truck fleet maintenance costs using interaction terms and stepwise regression analysis (Data file) |
| Unit 4. Analyzing Data with Nonlinear Models. Students learn to build models by
linearizing non-proportional data and learn how to interpret these in realistic situations.
| ||
| Chapter | Content | Memo Regarding |
| 11. Graphical Approaches to Nonlinear Data | Examining a variety of nonlinear graphical models with one independent variable (logarithmic, exponential, square, square root and reciprocal) and their transformations | Analyzing various data sets from a customer who wants better models for each set than those created by basic trendlines; this is accomplished by shifting and scaling the basic models and computing the goodness of fit for each (Data file) |
| 12. Modeling with Nonlinear Data | Building and interpreting nonlinear regression models, including general power models and multiplicative models in several variables | Creating and comparing multivariable models (one linear and one multiplicative) to help analyze operating costs at an insurance company (Data file) |
| 13. Nonlinear Multivariable Models | Extending the variety of nonlinear multivariable models to include quadratic models developed from interaction terms | Developing more accurate models of the commuter rail system data by using quadratic interaction terms (Data file) |
| Unit 5. Analyzing Data Using Calculus Models. Now that students understand how to
build models from data, they learn how to use concepts from calculus to understand the
problem from which the data and the model were derived.
| ||
| Chapter | Content | Memo Regarding |
| 14. Optimization and Analysis of Models | Using calculus (derivatives) to interpret and optimize polynomial and power models | Developing and optimizing a mathematical model to challenge an interpretation of a data set (Create your own data file) |
| 15. Deeper Exploration of Logs and Exponentials | Applying calculus to the analysis and optimization of logarithmic and exponential models | Applying calculus skills to exponential functions in order to help a wine collector plan her wine storage for the future (Create your own data file) |
| 16. Optimization in Several Variables | Defining constraints and performing constrained optimization using the SOLVER routine | Determining optimal mix of advertising budget under uncertain conditions, using Solver (Data file) |
| 17. Area Under the Curve | Evaluating definite integrals using both the Fundamental Theorem of Calculus and numerical methods to find the area under a curve. | Finding the area between curves to resolve a pricing dispute for a doll at Cool Toys for Tots (consumers’ and producers’ surplus). (Data file) |