📋 Statistics Probability

Part 1 of 7 — Mean, Median, Mode

Mean = sum/count; Median = middle value (sorted); Mode = most frequent.

Weighted average: multiply each value by its weight, then divide by total weight.

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Key Insight: Effect of adding/removing values: track the sum.

ACT Tip: Range = max - min.

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Data Displays

Part 2 of 7 — Data Displays

Bar graphs, histograms, line graphs, pie charts, stem-and-leaf plots.

Read axes labels and scales carefully.

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Key Insight: Box plots: min, Q1, median, Q3, max.

ACT Tip: Histograms show frequency distribution — bars touch (no gaps).

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Counting Principles

Part 3 of 7 — Counting Principles

Fundamental counting principle: if event A has m outcomes and B has n outcomes, together they have m × n outcomes.

Tree diagrams help visualize sequential events.

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Key Insight: With replacement: probabilities stay the same.

ACT Tip: Without replacement: probabilities change (dependent events).

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Basic Probability

Part 4 of 7 — Basic Probability

P(event) = 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|A).

ACT Tip: Complement: P(not A) = 1 - P(A).

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Combinations & Permutations

Part 5 of 7 — Combinations & Permutations

Permutation (order matters): nPr = n!/(n-r)!.

Combination (order doesn't matter): nCr = n!/[r!(n-r)!].

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Key Insight: Factorial: n! = n × (n-1) × ... × 2 × 1.

ACT Tip: ACT tip: ask "does order matter?" to decide which formula to use.

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Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

Permutation (order matters): nPr = n!/(n-r)!.

Combination (order doesn't matter): nCr = n!/[r!(n-r)!].

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Key Insight: Factorial: n! = n × (n-1) × ... × 2 × 1.

ACT Tip: ACT tip: ask "does order matter?" to decide which formula to use.

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Review & Applications

Part 7 of 7 — Review & Applications

Permutation (order matters): nPr = n!/(n-r)!.

Combination (order doesn't matter): nCr = n!/[r!(n-r)!].

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Key Insight: Factorial: n! = n × (n-1) × ... × 2 × 1.

ACT Tip: ACT tip: ask "does order matter?" to decide which formula to use.

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