AP Statistics Units 1-9 Lecture Notes

Unit 1: Introduction to Statistics

Types of Data

• Quantitative Data
  • Deals with numbers (e.g., heights, class size)
  • Represented numerically
• Categorical Data
  • Deals with names or labels (e.g., eye color, hair color)
  • Represented using two-way tables

Two-Way Tables

• Used for representing categorical data
• Shows intersections between variables
• Marginal Relative Frequency: Percentage of data in a single row/column compared to total
• Joint Relative Frequency: Percentage of data in a single group compared to total
• Conditional Relative Frequency: Percentage of data in a category given a specific group

Describing Quantitative Data

• C-SOCCS: Context, Shape, Outliers, Center, Spread
  • Shape: Symmetrical, skewed, unimodal, bimodal
  • Outliers: Points far from the rest
  • Center: Mean or median
  • Spread: Range, standard deviation, IQR

Basic Terms

• Mean: Average value
• Standard Deviation: Measure of variation
• Median: 50th percentile
• Range: Max value - Min value

Box Plots

• Five Number Summary: Minimum, Q1, Median, Q3, Maximum
• IQR (Interquartile Range): Q3 - Q1
• Identifying Outliers:
  • Low-end: Less than Q1 - 1.5*IQR
  • High-end: More than Q3 + 1.5*IQR

Normal Distributions

• Density Curve: Area of 1, shows probability distribution
• 68-95-99.7 Rule:
  • 68% within 1 SD
  • 95% within 2 SD
  • 99.7% within 3 SD

Unit 2: Describing Relationships

Scatterplots and Correlation

• SEED: Strength, Explanatory variable, Outliers, Direction
• Correlation Coefficient (R): Range from -1 to 1
  • Closer to -1 or 1 indicates stronger correlation

Regression Lines

• Line of Best Fit: Helps estimate values
• Residuals: Degree of error
  • Negative residual: Overestimated
  • Positive residual: Underestimated

Least Squares Regression Line

• Minimizes sum of squared residuals
• R-squared Value: Proportion of variance explained

Unit 3: Data Collection

Sampling Methods

• Simple Random Sample (SRS): Equal chance of selection
• Stratified Random Sample: Split into strata, randomly selected
• Cluster Sample: Split into heterogeneous groups, select entire clusters
• Systematic Sample: Select at set intervals

Bad Sampling Methods

• Convenience Sample: Easy to reach
• Voluntary Response Sample: Participants choose to respond

Observational Studies vs. Experiments

• Observational Study: No influence, collect data
• Experiment: Manipulate variables, apply treatments
• Principles of Experiments: Comparison, random assignment, control, replication

Unit 4: Probability and Random Variables

Probability Basics

• Probability between 0 and 1
• Simulation: Model to estimate probabilities

Probability Rules

• Mutually Exclusive: Cannot occur together
• Independent Events: Outcome of one does not affect the other

Random Variables

• Discrete: Countable values
• Continuous: Any value within an interval

Binomial and Geometric Variables

• Binomial: Fixed number of trials
• Geometric: Trials until first success

Unit 5: Sampling Distributions

Statistics vs. Parameters

• Statistic: Describes a sample
• Parameter: Describes a population

Sampling Distribution

• Probability distribution of a statistic
• Unbiased Estimator: Statistic equals parameter

Conditions for Sampling

• Random sampling, 10% condition, large counts

Unit 6: Inference for Categorical Data

Confidence Intervals

• Panic: Parameter, Assumptions, Name, Interval, Conclusion
• Interval estimation for population parameter

Significance Tests

• Phantoms: Parameter, Hypothesis, Assumptions, Name, Test statistic, Obtain p-value, Make decision, State conclusion

Unit 7: Inference for Quantitative Data

Confidence Intervals for Means

• Similar to proportions but use T-distribution
• Degrees of Freedom: n - 1

Significance Tests for Means

• T-Test: Test hypothesis about population mean

Unit 8: Categorical Data Analysis

Chi-Square Tests

• Goodness of Fit: Observed vs. expected distribution
• Homogeneity: Distribution across several populations
• Independence: Association between categorical variables

Unit 9: Inference for Slope

Linear Regression

• Slope (Beta): Estimate using sample data
• Confidence intervals and significance testing for slope
• Degrees of Freedom: n - 2

These notes cover the essential topics and key concepts from the AP Statistics lecture series, providing a comprehensive overview for each unit. This summary acts as a study aid for revisiting major themes and preparing for exams.