Data Interpretation and Statistical Reasoning

Scatterplots and Lines of Best Fit

The SAT presents scatterplots with a line (or curve) of best fit and asks you to:

1. Describe the association: positive, negative, or no association; linear or nonlinear
2. Interpret the slope: "For each additional year of experience, the predicted salary increases by $2{,}400" — that's the slope in context
3. Interpret the y-intercept: The predicted value when the x-variable is zero (sometimes this is meaningful, sometimes not)
4. Make a prediction: Use the line to estimate a y-value for a given x, or vice versa
5. Identify outliers: Points far from the line of best fit

Strategy: Always read axis labels first. The SAT relies on students misreading which variable is on which axis.

Two-Way Frequency Tables

These tables cross-tabulate two categorical variables. The SAT asks three types of questions:

Question Type	What It's Asking
Joint frequency	A specific cell value (e.g., "How many female students chose biology?")
Marginal frequency	A row or column total
Conditional probability	"Given that a student is female, what fraction chose biology?" = cell / row total

Critical distinction: "What fraction of biology students are female?" (cell / column total) vs. "What fraction of female students chose biology?" (cell / row total). The SAT always includes both interpretations as answer choices.

Statistical Inference

The SAT tests conceptual understanding of:

• Margin of error: A larger sample size → smaller margin of error. The population proportion is likely within the interval (estimate ± margin of error).
• Confidence intervals: "95% confident" means that 95% of samples of this size would produce an interval containing the true value.
• Sampling bias: The sample must be randomly selected from the population to generalize. Convenience samples, voluntary response, and self-selected samples are biased.
• Correlation vs. causation: An observational study can show association but not causation. Only a randomized controlled experiment can establish causation.

SAT Pattern: "A researcher surveys 200 students at a university and finds 60% support a new policy. Which conclusion is valid?"

The valid conclusion depends on how the sample was selected. If random: "Approximately 60% of students at this university support the policy." If not random: no valid generalization beyond the sample.