Name: Combining Random Variables
Uploaded: 2020-05-04T23:00:00.000Z
Description: In this stream, we discuss transforming random variables and combining random variables, along with some modified review questions in preparation for the modified 2020 AP Statistics exam.

AP Statistics

Dive into unit 1 of AP Statistics: Exploring One Variable Data! Start the course by learning about displaying and describing categorical data, normal distributions, and analyzing graphs. With these helpful study guides, review videos, and slides, you'll be prepared to do well on the AP exam!

Unit 1 – Exploring One-Variable Data

This is an overview of unit 2 of AP Statistics: Exploring Two Variable Data. Dive into bivariate data, causation vs. correlation, residuals, and linear regression models and build upon your unit 1 knowledge!

Unit 2 – Exploring Two-Variable Data

Dive into unit 3 of AP Statistics: Collecting Data! Learn how to design and plan experiments and studies and how to choose sampling data. We also go over source bias and causation vs. correlation.

Unit 3 – Collecting Data

Explore unit 4 of AP Statistics: Probability. Learn all about the binomial distribution, binomial and geometric distributions, conditional probability, and mutually exclusive events!

Unit 4 – Probability, Random Variables, & Probability Distributions

Master unit 5 of AP Statistics: Sampling Distributions with our extensive resources! Learn about the cental limit theorem, point estimates, and how to use sampling distributions for sample means and proportions with our resources! 

Unit 5 – Sampling Distributions

Dig deep into unit 6 of AP Statistics—Inference for Categorical Data: Proportions. Set up confidence intervals and become a pro at conducting significance tests for proportions!

Unit 6 – Proportions

This is an overview of unit 7 of AP Statistics—inference for qualitative data: means. Build upon unit 6 and learn how to set up confidence intervals and significance tests for means! We also have resources to help you gauge when and how to use t and z tests.

Unit 7 – Means

Master unit 8 of AP Statistics—inference for categorical data: chi square! With our comprehensive resources, learn how to use the chi-square statistic for hypothesis testing! We also cover how to use the formula sheet on test day.

Unit 8 – Chi-Squares

Finish up AP Stats with unit 9\—inference for quanitative data: slopes. Learn how to set up confidence intervals and conduct significance tests for slopes of regression models! Use our resources to review important formulas and equations and become prepared for exam day!

Unit 9 – Slopes

Frequently Asked Questions

Previous Exam Prep

AP Cram Sessions 2021

Live Cram Sessions 2020

January

Past Events

Study Tools

Exam Skills

In this stream, we discuss transforming random variables and combining random variables, along with some modified review questions in preparation for the modified 2020 AP Statistics exam.

What is Statistics?

Quantitative Data

Categorical Data

What's the Point of Statistics?

Context of Data

Describing Data

Unit 1 Overview: Exploring One-Variable Data

Statistics & Data, Data, Data

Going Deeper into Data and the "W"s

(1) Who 

(2) What 

(3) When and Where

(4) Why 

(5) How

Key Vocabulary

Introducing Statistics: What Can We Learn from Data?

Intro to Z-Scores

Normal Model: More than Just a Hump

Standard Normal Model

The Empirical (68–95–99.7) Rule

Practice Problems

Answers

The Normal Distribution

Types of Variables

Going Deeper: Categorical vs. Quantitative Variables

Example Question

The Language of Variation: Variables

Frequency Tables

Extension: Relative Frequency Tables

Summary

Representing a Categorical Variable with Tables

Bar Graphs

Pie Charts

Contingency Table (Two-Way Table)

Real-Life Applications: To Trust or Not To Trust a Bar/Pie Chart?

Representing a Categorical Variable with Graphs

Histograms

Frequency Polygons

Cumulative graphs (Ogives)

Stem-and-Leaf Plots (Stemplots)

Dotplots

Representing a Quantitative Variable with Graphs

Shape

Center

Spread

Describing the Distribution of a Quantitative Variable

Statistics of Center

The Mean

The Median

Statistics of Spread

Standard Deviation

Interquartile Range (IQR)

A Note About Outliers

Method I: 1.5 x IQR 

Method II: Standard Deviations

Resistance and Nonresistant Measures

Summary Statistics for a Quantitative Variable

Five Number Summaries

Box Plots

Box Plots and Skew

Practice Questions

Graphical Representations of Summary Statistics

Comparing Groups with Stem-and-Leaf Plots: Warm Up

Comparing Groups with Histograms: Practice AP-Style Problem

Comparing Groups with Box Plots: Practice AP-Style Problem

Comparing Distributions of a Quantitative Variable

Exam Weighting

Bivariate Data 🧠

Categorical 

Quantitative

Computer Outputs 🖥️

Mathematical Practices 🧮

Main Ideas for this Unit

Unit 2 Overview: Exploring Two-Variable Data

Types of Data 

Bivariate Categorical Data

Bivariate Quantitative Data

How Can I Use This Data?

Introducing Statistics: Are Variables Related?

Various Tables and Diagrams

Two-Way Tables

Side-by-Side Bar Graphs

Segmented Bar Graphs

Mosaic Plots

Determining Associations from Graphical Representations

Representing Two Categorical Variables

Additional Relative Frequencies

Marginal Relative Frequency

Conditional Relative Frequency

Determining Associations from a Two-Way Table

Example

Vocabulary Practice from 2.1 to 2.3 Material

Statistics for Two Categorical Variables

What is a Scatterplot? ❓

Describing Scatterplots 🗒️

Form

Direction

Strength

Unusual Features

Side Note: Outliers, Influential Points, and (High) Leverage Points

Representing the Relationship Between Two Quantitative Variables

Examples

Calculating the Correlation Coefficient

Correlation

What is a LSRL?

Extrapolation

Practice Problem

Answer

Linear Regression Models

Residual Plots

Example 1

Example 2

Good or Bad? 🧐

Calculating Residuals

Residuals

LSRL—Slope

Template for Interpretation

LSRL—y-intercept

LSRL—Coefficient of Determination

LSRL—Standard Deviation of the Residuals

Reading a Computer Printout

Least Squares Regression

Influential Points

Outliers

High-Leverage Points

Transforming Data and Nonlinear Regression

Exponential Models

Power Models

How Can I Tell, Then?

Analyzing Departures from Linearity

How Do We Approach Data Collection?

Data Collection and "Randomness"

Planning a Study

Random Sampling and Data Collection

Biases

Experimental Design

Unit 3 Overview: Collecting Data

📊 Data: Truth-Revealing or Deceiving?

Examples of Unreliable Sampling

Examples of Reliable Sampling

Introducing Statistics: Do the Data We Collected Tell the Truth?

Important Vocabulary

Introduction to Planning a Study

Types of Non-Biased Sampling Methods 

Simple Random Sample (SRS)

Stratified Random Sample

Cluster Sample

Systematic Random Sample

Bias in Sampling 

Voluntary Response

Undercoverage

Nonresponse

Wording in Questions

Convenience Sampling

Why does this matter, then? 

Potential Problems with Sampling

🗃 Components of an Experiment

Confounding

🖋 Elements of a Well-Designed Experiment

🗄 Types of Experiments

Blind Experiments

Completely Randomized Design

Randomized Block Design

Matched Pairs

Introduction to Experimental Design

Essential Knowledge

The Big Three

Selecting an Experimental Design

Inferences for Studies/Samples

Inferences for Experiments

Inference and Experiments

Probability: What are the Odds?

Categorical Variables

Unit 4 Overview:  Probability, Random Variables, and Probability Distributions

Combining Random Variables

Combining Random Variables

Resources

Combining Random Variables

Resources

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