Problem-Solving and Data Analysis — one screen
≈15% of Math · 5–7 questions · seven skills, and the fastest points on the section once the vocabulary is learned. Almost every question is arithmetic wearing a lab coat.
The seven skills
| Skill | The move |
|---|---|
| Ratios, rates, proportions, units | Set up a proportion; cancel units |
| Percentages | Multiply by a factor, never add a percentage |
| One-variable data | Mean, median, range, spread |
| Two-variable data | Scatterplots, line of best fit, prediction |
| Probability | Count the favourable, divide by the total |
| Inference and margin of error | What a sample says about a population |
| Evaluating statistical claims | What a study design does and does not permit |
Percentages, as multipliers
| English | Multiplier |
|---|---|
| increase by 20% | × 1.20 |
| decrease by 20% | × 0.80 |
| 20% of | × 0.20 |
| two successive: +20% then −10% | × 1.20 × 0.90 = × 1.08 |
| reverse: 84 is 70% of what? | ÷ 0.70 |
Statistics vocabulary
| Term | Meaning |
|---|---|
| Mean | Total ÷ count. Moves when an outlier is added |
| Median | Middle value in order. Barely moves |
| Range | Largest − smallest |
| Standard deviation | How spread out. Tighter cluster = smaller |
Skewed by a few very large values: mean > median. Symmetric: they are about equal.
Sampling — the two random questions
| What was random | What it licenses |
|---|---|
| Random selection from a population | Generalising to that population |
| Random assignment to groups | Concluding cause and effect |
Neither one → describe only what was observed. A survey of gym members says nothing about the town.
Margin of error gives a plausible range for the population value: 42% ± 3% means 39% to 45%. Bigger sample → smaller margin. It never says anything about how honest the answers were.
Where points go
- Adding two percentage changes instead of multiplying the factors.
- Taking the percentage of the new value when the question means the original.
- Treating an observational study as evidence of cause.
- Generalising from a sample that was not randomly selected.
- Using the mean where the question asked for the median.
- Ignoring the units — per hour against per minute, km against m.
Educerie · written from the published College Board Assessment Framework for the Digital SAT Suite (Math, Problem-Solving and Data Analysis). Original text. Last reviewed 12 September 2026.