AP Statistics Unit Notes

Unit 1: Basics of Data

Types of Data

• Quantitative Data:
  • Deals with numbers (e.g., heights, class size).
• Categorical Data:
  • Deals with names and labels (e.g., eye color, hair color).
  • Represented using a two-way table.

Two-Way Table

• Shows intersections between two variables.
• Marginal Relative Frequency: Percent of data in a single row/column compared to the total.
• Joint Relative Frequency: Percent of data in a single group compared to total.
• Conditional Relative Frequencies: Percent of data in a category when given a specific group.

Describing Quantitative Data

• Use C-SOCS acronym:
  • Context
  • Shape (symmetrical, skewed, peaks)
  • Outliers
  • Center (mean, median)
  • Spread (range, standard deviation, IQR)

Basic Statistical Terms

• Mean: Average value.
• Standard Deviation: Measure of variation.
• Median: 50th percentile.
• Range: Max value minus min value.

Box Plots

• Five Number Summary: Minimum, Q1, Median, Q3, Maximum.
• IQR (Interquartile Range): Q3 - Q1.
• Outliers:
  • Low-End Outliers: < Q1 - 1.5(IQR)
  • High-End Outliers: > Q3 + 1.5(IQR)

Distribution

• Percentile: Percentage of values less than or equal to a specific value.
• Cumulative Relative Frequency: Cumulative percentages from intervals.
• Z-Scores: Number of standard deviations a value is from the mean.

Transforming Data

• Adding/Subtracting: Shape/Variability same, Center shifts.
• Multiplying/Dividing: Shape same, Center/Variability scales.

Density Curves & Normal Distribution

• Probability distribution with area of 1.
• 68-95-99.7 Rule:
  • 68% within 1 SD
  • 95% within 2 SDs
  • 99.7% within 3 SDs

Unit 2: Correlation and Regression

Describing Scatter Plots

• Use C-DOTS acronym:
  • Context
  • Direction (positive/negative)
  • Outliers
  • Type (linear/nonlinear)
  • Strength

Correlation (R Value)

• Range: -1 to 1. Closer to ±1 indicates stronger correlation.
• R Value Affects:
  • Not affected by changing units or axes.
  • Outliers within pattern strengthen R.
• Correlation ≠ Causation

Regression Lines

• Equation: ( ŷ = a + bx )
• Residuals: Difference between actual and predicted values.
• Least Squares Regression Line: Minimizes sum of squared residuals.
• S Value: Average distance predicted values away from LSR.
• R² Value: Coefficient of determination.

Outliers & Influence

• Outliers can impact regression line slope/intercept.

Residual Plots

• Detects linearity of data fit.

Unit 3: Sampling and Experimentation

Sampling Methods

• Simple Random Sample (SRS): Equal chance for all members.
• Stratified Random Sample: Population divided into homogeneous groups.
• Cluster Sample: Population split into clusters; entire clusters surveyed.
• Systematic Sample: Selects individuals at set intervals.

Bad Sampling Methods

• Convenience Sample: Easy-to-reach individuals.
• Voluntary Response Sample: Self-selected participation.
• Biases: Undercoverage, Nonresponse, Response Bias, Wording Influence.

Observational Studies vs. Experiments

• Observational: Collect data without influence.
• Experiment: Manipulate variables, apply treatments.

Experimental Design Principles

• Comparison, Random Assignment, Control, Replication

Unit 4: Probability and Random Variables

Probability Basics

• Probability Range: 0 to 1.
• Simulation Models: Mimic real-world events.

Probability Rules

• Mutually Exclusive: No overlap.
• Independent Events: Outcome of one doesn't affect the other.

Types of Random Variables

• Discrete: Countable values.
• Continuous: Any value in a range.
• Binomial & Geometric: Specific conditions.

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(Notes continue for Units 5-9)

These notes are designed to provide a comprehensive overview of key concepts in AP Statistics, with details on data types, sampling methods, probability rules, and more. Use this as a study guide to reinforce understanding of statistical principles and for exam preparation.