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# Problem Solving and Data Analysis

The Math Tests in the SAT Suite of Assessments reflect research that has identified what is essential for college readiness and success. The tests require problem solving and data analysis: the ability to create a representation of a problem, consider the units involved, attend to the meaning of quantities, and know and use different properties of operations and objects. Problems in this category will require significant quantitative reasoning about ratios, rates, and proportional relationships and will place a premium on understanding and applying unit rate.

Students will be expected to identify quantitative measures of center, overall patterns, and any striking deviations from the overall pattern and spread in one or two different data sets. This includes recognizing the effects of outliers on the measures of center of a data set.

All Problem Solving and Data Analysis questions test the ability of students to use their math understanding and skills to solve problems they could encounter in the real world. Many of these problems are set in academic and career contexts and are likely to draw from science and social science.

Problem Solving and Data Analysis is one of the three SAT Suite Math subscores, reported on a scale of 1 to 15.

This domain will feature multiple-choice and student-produced response question types. Calculator use is always permitted, but not always needed or recommended.

Problem Solving and Data Analysis questions ask students to:

1. Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems. The student will use a proportional relationship between two variables to solve a multistep problem to determine a ratio or rate; calculate a ratio or rate and then solve a multistep problem; or take a given ratio or rate and solve a multistep problem.
2. Solve single- and multistep problems involving percentages. The student will solve a multistep problem to determine a percentage; calculate a percentage and then solve a multistep problem; or take a given percentage and solve a multistep problem.
3. Solve single- and multistep problems involving measurement quantities, units, and unit conversion. The student will solve a multistep problem to determine a unit rate; calculate a unit rate and then solve a multistep problem; solve a multistep problem to complete a unit conversion; solve a multistep problem to calculate density; or use the concept of density to solve a multistep problem.
4. Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related. The student will, given a scatterplot, select the equation of a line or curve of best fit; interpret the line in the context of the situation; or use the line or curve of best fit to make a prediction.
5. Use the relationship between two variables to investigate key features of the graph. The student will make connections between the graphical representation of a relationship and properties of the graph by selecting the graph that represents the properties described, or using the graph to identify a value or set of values.
6. Compare linear growth with exponential growth. The student will infer the connection between two variables given a context in order to determine what type of model fits best.
7. Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability. The student will summarize categorical data or use categorical data to calculate conditional frequencies, conditional probabilities, association of variables, or independence of events.
8. Make inferences about population parameters based on sample data. The student will estimate a population parameter given the results from a random sample of the population. The sample statistics may mention confidence intervals and measurement error that the student should understand and make use of, but need not calculate.
9. Use statistics to investigate measures of center of data and analyze shape, center, and spread. The student will calculate measures of center and/or spread for a given set of data or use given statistics to compare two separate sets of data. The measures of center that may be calculated include mean, median, and mode, and the measures of spread that may be calculated include range. When comparing two data sets, the student may investigate mean, median, mode, range, and/or standard deviation.
10. Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods. The reports may consist of tables, graphs, or text summaries.