2.0 Unit 2 Overview: Exploring Two-Variable Data

Exam Weighting

• 5-7% of the test

• Roughly 2 to 3 multiple choice questions

Developing Understanding 🧠

After covering single-variable statistics, it’s time to increase the complexity a little bit with two variable statistics! We can deal with two variable statistics in two ways. With categorical variables, we can use two way tables to represent the relationship between two different categories of categorical variables. With quantitative variables, we can show the relationship between these using scatterplots. We will also see whether there is a relationship between two variables in both situations. This will link to later units as well. Our study of two-way tables will link to probability (Unit 4) and Chi-squared tests for homogeneity or independence (Unit 8). Our study of scatterplots will link to regression inference as well (Unit 9).

Mathematical Practices

Three of the College Board's mathematical practices for AP Statistics are used in this unit, which will be outlined below.

1. Selecting Statistical Methods

This is useful when we decide whether we want to use two-variable statistics methods and the type to use or to use inference techniques learned later on.

1. Data Analysis

Using data analysis, we’ll figure out how to figure out different statistics from two-variable data sets and also find ways to model with them and draw conclusions.

1. Statistical Argumentation

In this unit, we will learn to argue about the strength of how much variables are related to each other, and also the most important sentence of this unit: correlation does not imply causation!

Main Ideas for this Unit

• Categorical Variables

• Two Way Tables

• Joint Relative Frequencies

• Marginal Relative Frequencies

• Conditional Relative Frequencies

• Side-by-side bar graphs

• Segmented bar graphs

• Mosaic plots

• Correlation

• Quantitative Variables

• Scatterplots

• Form

• Direction

• Strength

• Unusual features (gaps, clusters, outliers)

• Correlation Coefficient

• Linear Regression (Least Squares Regression)

• Extrapolation

• Residuals

• r, R^2. and s

• Influential Points

• Transforming Data Sets