SAT Math — Data, Statistics, and Geometry Quick Reference

Core Concepts

Statistics: Measures of Center and Spread

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When to use median vs. mean:

Income, home prices, other skewed data → median

Symmetric, no outliers → mean is fine

Outlier effect on mean:

One extreme high value → pulls mean UP

One extreme low value → pulls mean DOWN

Sampling and Inference

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Data Interpretation: Tables and Graphs

Two-way table percentages:

"% of X that are Y" → Y/X row or column total (NOT grand total)

"% of TOTAL that are Y" → Y/grand total

Scatterplot reads:

Direction: positive (both rise) or negative (one rises as other falls)

Strength: tight cluster = strong; scattered = weak

Line of best fit: y = mx + b; slope = predicted change per unit of x

Outlier: point far from the trend line

CRITICAL: Correlation ≠ causation

Geometry

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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°

Trig (SOH CAH TOA):

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

Angle rules:

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

Math: Data & Problem Solving