📝 Data Statistics

Part 1 of 7 — Mean, Median, Mode

Mean (average): sum of values / number of values.

Median: middle value when sorted (average of two middle if even count).

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Key Insight: Mode: most frequent value.

SAT Tip: SAT tip: adding/removing values changes mean — track the sum.

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Standard Deviation & Spread

Part 2 of 7 — Standard Deviation & Spread

Range = max - min.

Standard deviation measures spread from the mean.

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Key Insight: Larger SD = more spread out; smaller SD = more clustered.

SAT Tip: SAT won't ask you to calculate SD, but you must compare or interpret it.

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Data Displays

Part 3 of 7 — Data Displays

Histograms: bars show frequency for intervals (no gaps).

Box plots: show min, Q1, median, Q3, max.

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Key Insight: IQR = Q3 - Q1 (middle 50% of data).

SAT Tip: Outliers: typically more than 1.5 × IQR below Q1 or above Q3.

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Scatterplots & Line of Best Fit

Part 4 of 7 — Scatterplots & Line of Best Fit

Scatterplot: shows relationship between two variables.

Line of best fit: approximates the trend.

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Key Insight: Positive correlation: both increase together; negative: one up, one down.

SAT Tip: r (correlation coefficient): closer to ±1 = stronger linear relationship.

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Probability Basics

Part 5 of 7 — Probability Basics

Probability = favorable outcomes / total outcomes.

P(A or B) = P(A) + P(B) - P(A and B).

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Key Insight: P(A and B) = P(A) × P(B) if independent.

SAT Tip: Conditional probability: P(A|B) = P(A and B) / P(B).

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Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

Probability = favorable outcomes / total outcomes.

P(A or B) = P(A) + P(B) - P(A and B).

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Key Insight: P(A and B) = P(A) × P(B) if independent.

SAT Tip: Conditional probability: P(A|B) = P(A and B) / P(B).

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Review & Applications

Part 7 of 7 — Review & Applications

Probability = favorable outcomes / total outcomes.

P(A or B) = P(A) + P(B) - P(A and B).

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Key Insight: P(A and B) = P(A) × P(B) if independent.

SAT Tip: Conditional probability: P(A|B) = P(A and B) / P(B).

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