Problem-Solving and Data Analysis The quantitative-reasoning sixth of the paper, and the widest set of skills per question. Ratios and units, percentages, one- and two-variable data, probability, margins of error, and the study-design questions almost nobody revises.
The course — 7 units, in order
01 Ratios, Rates, Proportional Relationships and Units Splitting a total by a ratio, using a rate across a unit change, and the proportional relationships that pass through the origin — plus the unit conversions that cost more points here than the mathematics does. Start 02 Percentages Percent change as a multiplier, reversing a change to find the original amount, successive changes that multiply rather than add, and the question behind every hard percentage item: a percentage of WHAT? Start 03 One-Variable Data: Distributions and Measures of Center and Spread Mean against median and which one an outlier moves, means handled through totals, frequency tables, skew read off two numbers, and standard deviation compared rather than computed — because the test never asks you to compute one. Start 04 Two-Variable Data: Models and Scatterplots Reading a line of best fit in the context's own units, telling interpolation from extrapolation, residuals and what their sign and pattern reveal — and the reason a scatterplot can never establish cause. Start 05 Probability and Conditional Probability Probability read off a two-way table, the addition rule that subtracts the overlap, and the conditional questions where the denominator shrinks to a single row or column — including why the two directions of a conditional are different numbers. Start 06 Inference from Sample Statistics and Margin of Error Turning a sample estimate into an interval, deciding which claims that interval supports, and the square-root law that makes precision expensive — plus the bias no sample size can fix. Start 07 Evaluating Statistical Claims: Observational Studies and Experiments Two independent questions decide what any study may claim: was the sample randomly selected, and were the treatments randomly assigned. One buys generalisation, the other buys causation, and neither substitutes for the other. Start