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Math: Data & Problem Solving
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SAT Math — Data, Statistics, and Geometry Quick Reference
Core Concepts
Statistics: Measures of Center and Spread
| Measure | Definition | Sensitive to Outliers? |
| Mean | Sum ÷ count | YES — outliers pull it |
| Median | Middle value (data ordered) | NO — robust to outliers |
| Mode | Most frequent value | No |
| Range | Max − Min | YES |
| Standard deviation | Spread from mean | YES |
| Concept | Rule | |
| Random sample | Can generalize results to the population | |
| Non-random sample | Cannot generalize; results may be biased | |
| Voluntary response bias | Strong-opinion respondents overrepresented | |
| Convenience sampling | Easy-to-reach sample; may not represent population | |
| Margin of error | Uncertainty range; 60% ± 3% means 57–63% | |
| Inference | You can only infer about the POPULATION the sample was drawn from | |
| Formula | Use | |
| Pythagorean theorem: a² + b² = c² | Right triangle; c = hypotenuse | |
| 30-60-90 sides: x : x√3 : 2x | Special right triangle | |
| 45-45-90 sides: x : x : x√2 | Special right triangle | |
| Area of circle: πr² | ||
| Circumference: 2πr | ||
| Area of triangle: ½bh | ||
| Volume of cylinder: πr²h | ||
| Sum of triangle angles: 180° |
- sin = opposite/hypotenuse
- cos = adjacent/hypotenuse
- tan = opposite/adjacent
- Vertical angles: equal
- Supplementary: sum = 180°
- Parallel lines + transversal: alternate interior = equal; co-interior = 180°
Common Exam Traps
- Mean vs. median: The question might give you a dataset with one extreme outlier — median is usually the better descriptor
- Two-way table denominator: "What percent of males..." → use male row total, not grand total
- Correlation doesn't prove causation: Always a trap answer on data questions
- Standard deviation size: Larger SD = more spread; doesn't tell you anything about the mean
- 30-60-90 trap: Short leg is opposite 30°; long leg (×√3) is opposite 60°
- Trig functions: Make sure you know which angle you're working with and which sides are "opposite" and "adjacent" to THAT angle
- Circle area vs. circumference: πr² = area; 2πr = circumference (not πd = area — that's wrong)
- Volume formulas: Cone and pyramid BOTH use ⅓ × base area × height
Aligned to the College Board Digital SAT specifications.
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