AP Statistics Unit 1-9 Lecture Notes

Unit 1: Introduction to Statistics

Categorical vs Quantitative Data

• Quantitative Data: Deals with numbers (e.g., heights, class size).
• Categorical Data: Deals with labels (e.g., eye color, hair color).

Representing Categorical Data

• Two-Way Table: Represents intersection between two variables.

Key Terms

• Marginal Relative Frequency: Percentage of data in a row/column compared to the total.
• Joint Relative Frequency: Percentage data of a group compared to total.
• Conditional Relative Frequencies: Percentage in a category given a specific group.

Quantitative Data Analysis

• C-SOCS Acronym:
  • C: Context
  • S: Shape (symmetrical, skewed)
  • O: Outliers
  • C: Center (mean, median)
  • S: Spread (range, standard deviation, IQR)

Important Concepts

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

Box Plots and IQR

• Five Number Summary: Minimum, 25th percentile (Q1), Median, 75th percentile (Q3), Maximum.
• IQR: Q3 - Q1.
• Outliers: Values less than Q1-1.5(IQR) or greater than Q3+1.5(IQR).

Normal Distribution

• Density Curve: Shows probability distribution.
• 68-95-99.7 Rule: Standard deviations from the mean.

Unit 2: Correlation and Regression

Scatterplots

• SEED Acronym:
  • S: Shape
  • E: Explanatory variable
  • E: Emphasize outliers
  • D: Direction

Correlation Coefficient (R)

• Ranges from -1 to 1. Closer to -1 or 1 indicates stronger correlation.

Regression Lines

• Equation: ( \hat{y} = a + bx )
• Residual: Actual value minus Predicted value.

Least Squares Regression Line

• Minimizes sum of squared residuals.

Unit 3: Sampling and Experimental Design

Sampling Methods

• Simple Random Sample: Every member has equal chance.
• Stratified Random Sample: Population divided into strata.
• Cluster Sample: Entire clusters selected.
• Systematic Random Sample: Select individuals at set intervals.

Experimental Design Principles

• Comparison, Random Assignment, Control, Replication.

Unit 4: Probability and Random Variables

Probability Basics

• Mutually Exclusive: Events cannot occur simultaneously.
• Independence: Outcome of one does not affect the other.

Probability Rules

• Complement Rule: ( P(A') = 1 - P(A) )

Random Variables

• Discrete: Countable values.
• Continuous: Any value within a range.

Unit 5: Sampling Distributions

Key Concepts

• Statistic vs Parameter: Sample vs Population.
• Central Limit Theorem: Sampling distribution becomes normal as sample size increases.

Unit 6: Inference for Proportions

Confidence Intervals

• Panic Acronym: Parameter, Assumptions, Name, Interval, Conclusion.

Significance Tests

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

Unit 7: Inference for Means

Key Concepts

• Use of T-distributions.
• Degrees of Freedom: ( n - 1 ).

Unit 8: Chi-Squared Tests

Types of Tests

• Goodness of Fit: Observed vs Expected distribution.
• Homogeneity: Distribution across groups.
• Independence: Association between two variables.

Unit 9: Inference for Slope

Key Concepts

• Confidence Interval & Significance Test for Slope: Determines linear relationship.
• Residual Plot: Determines fit of a linear model.

These notes cover the essential concepts and methodologies discussed in the transcript for AP Statistics. They summarize units 1 through 9 and include explanations for key statistical terms, techniques, and processes.