Chapter 17: Problem Solving and Data Analysis

Problem Solving and Data Analysis focuses on the quantitative reasoning and data interpretation competencies assessed in the Problem Solving and Data Analysis domain of the SAT Math Test. Students encounter questions that require analyzing ratios, rates, and proportional relationships in realistic contexts, often drawn from science, economics, social research, or workplace scenarios. A central skill involves extracting meaningful information from visual representations including graphs, tables, scatterplots, and other data displays to identify patterns, compare variables, and draw evidence-based conclusions. The chapter emphasizes constructing and evaluating mathematical models that represent real-world phenomena, then using these models to make predictions or explain observed behaviors. A crucial distinction addressed is recognizing the difference between values generated by a fitted model and actual collected data points, along with understanding the limitations and applications of statistical representations. Students develop statistical literacy by working with measures of center and spread, understanding correlation and causation, and interpreting the reliability of predictions based on sample data and model fit. Throughout the chapter, problems integrate multiple steps of mathematical reasoning, requiring students to translate between verbal descriptions and mathematical representations, perform calculations with appropriate units, and justify their conclusions based on quantitative evidence. The emphasis remains on mathematics as a practical tool for understanding complex real-world situations rather than abstract computation, preparing students for academic coursework and informed decision-making in professional and civic contexts.