AP Statistics Unit 1 Cheatsheet: Exploring One-Variable Data and Collecting Data

Population vs. Sample

• Population (N): All items/individuals of interest
• Sample (n): Subset selected from population for study
• Observational unit (individual): Single person or object on which one or more variables are measured
• Datum: Single piece of information; data = collection

Key Principle: Studies necessary when population too large or difficult to access completely.

In Context: Always connect statistical results back to real-world meaning.

Measures of Center

• Mean (x̄): x̄ = (1/n) Σ xᵢ; affected by outliers
• Median: Middle value when ordered; resistant to outliers

Quartiles & Percentiles

• Q1 (25th): Median of lower half
• Q2 (50th): Median of all data
• Q3 (75th): Median of upper half
• pth percentile: p% of data ≤ this value

Variability

• Range: Max − Min
• IQR: Q3 − Q1 (middle 50%)
• Std Dev (s): s = √[ (1/(n−1)) Σ (xᵢ − x̄)² ]

Outlier Detection

• > Q3 + 1.5(IQR) or < Q1 − 1.5(IQR)
• Values with |z| > 2 (i.e., > mean + 2s or < mean − 2s) are unusual/far from typical, but the AP outlier rule is the 1.5 × IQR rule: below Q1 − 1.5(IQR) or above Q3 + 1.5(IQR)

Sampling Methods

• Simple Random Sample (SRS): Every sample of size n has equal chance
• Stratified: Divide into homogeneous strata; randomly sample within each
• Cluster: Divide into clusters; randomly select clusters; collect from all units in selected clusters
• Systematic: Select every kth unit from random starting point
• With/without replacement: Unit returned or not after selection

Bias Types

• Voluntary response: Sample of volunteers only
• Undercoverage: Method excludes part of population
• Nonresponse: Failure to obtain responses from selected individuals
• Response: Responses differ from true value (confusing/leading questions, self-report)

Reducing Bias: Use random sampling; ensure high response rates; ask clear, neutral questions.