The main takeaway from this section should be knowing how to calculate and interpret the standard deviation and mean. 

of a discrete variable is its average value over many, many repetitions of the same chance process. To find the mean or expected value of X, multiply each possible value of X by its probability and then add all of the products. 

The mean is the balance point of a distribution. Formula: 

DO NOT write the mean of a random variable as a non integer value if it is a decimal because almost all expected values are decimals. 

Variability of a Discrete Random Variable

 standard deviation of a discrete random variable

 measures how much the values of the variable typically vary from the mean. 

The standard deviation of X is the square root of the variance so 

SD = sqrt(summation(xi-mean of x)^2 * pi)

If you decide to use your calculator, make sure you list how you got to your answer. Use context and don’t just put a number down as the answer. Show work to maximize the amount of points you get.

Probability: Random Variables, Binomial/Geometric Distributions

Mean and Standard Deviation of Random Variables

Administration 1

Administration 2

Administration 3

AP Stats Exam Prep 2020 | Reviews + Free Study Help | Fiveable

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

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

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

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, and Probability Distributions

Probability, Random Variables, and 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

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: Inference for Categorical Data: Proportions

Inference for Categorical Data: 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: Inference for Qualitative Data: Means

Inference for Qualitative Data: 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: Inference for Categorical Data: Chi-Square

Inference for Categorical Data: Chi-Square

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: Inference for Quantitative Data: Slopes

Inference for Quantitative Data: Slopes

With these resources, you'll be ready to ace the multiple choice question section on the AP Statistics exam! We cover key concepts, important equations, logistics, and even exam strategies. You'll also be able to practice your skills with practice questions and be ready for exam day!

Multiple Choice Questions (MCQs)

With our resources, learn how to master the free response question section on the AP Statistics exam featuring practice prompts with student responses and teacher feedback, logistics, key concepts, and helpful tips, you'll be ready to ace the exam. We also go through the rubric and key equations. 

Free Response Questions (FRQs)

Blogs

Exam Reviews 2020

Confused about something and have questions? Our comprehensive question and answer sessions are sure to help you answer those questions and prepare for the AP statistics exam! Come with your questions ready!

Q & A sessions

This is a thorough review of the AP Statistics course, including reviews of each of the units, key concepts, exam strategies, and other tips and tricks, you'll have everything you need to be prepared for any AP statistics exams!

Big Reviews: Finals & Exam Prep

AP Cram Sessions 2021

Live Cram Sessions 2020

March

February

December

November

October

September

Initial

January

Past Events

Your Guide to the 2021 AP Statistics Exam

Format of the 2021 AP Statistics Exam

Paper Exam:

Digital Exam: 

When is the 2021 AP Statistics exam and how do I take it?

How should I prepare for the exam?

Pre-work: set up your study environment

AP Statistics 2021 Study Plan

👆 UNIT 1: Exploring One-Variable Data

✌️ UNIT 2: Exploring Two-Variable Data

🔎 UNIT 3: Collecting Data

🎲 UNIT 4: Probability & Random Variables

📊 UNIT 5: Sampling Distributions

⚖️ UNIT 6: Inference for Categorical Data (Proportions)

😼 UNIT 7: Inference for Quantitative Data (Means)

✳️ UNIT 8: Inference for Categorical Data (Chi-Square)

📈 UNIT 9: Inference for Quantitative Data (Slopes)

2021 AP Statistics Exam Guide

Unit 1 Key Terms (15-23%): Exploring One-Variable Data

Unit 2 Key Terms (5-7%): Exploring Two-Variable Data

Unit 3 Key Terms (12-15%): Collecting Data

Unit 4 Key Terms (10-20%): Probability, Random Variables, and Probability Distributions

Unit 5 Key Terms (7-12%): Sampling Distributions

Unit 6 Key Terms (12-15%): Inference for Categorical Data: Proportions

Unit 7 Key Terms (10-18%): Inference for Quantitative Data: Means

Unit 8 Key Terms (2-5%): Inference for Categorical Data: Chi-Squared

Unit 9 Key Terms (2-5%): Inference for Quantitative Data: Slopes

Closing Thoughts

Best Quizlet Decks for AP Statistics

Overview 📈 

Data 📊

Resources to Dig Deeper 📚

Other Factors to Consider 🤔

Tips & Words of Wisdom 💬

Closing statement 💭

Is AP Statistics Hard? Is AP Statistics Worth Taking?

Overview of the AP Stats Free Response Questions

Section II of the AP Stats Exam: 6 free response questions

How to Rock the FRQs - Rubric

How to Rock the FRQs - The Process

Before you start writing

Formula Sheet for AP Statistics

Sample AP Stats FRQs 

AP Statistics Free Response Questions

What is Statistics?

Quantitative Data

Categorical Data

Context of Data

Describing Data

Unit 1 Overview: Exploring
One-Variable
Data

Intro to Statistics

Key Vocabulary

Introducing Statistics: What Can We Learn from Data?

Intro to Z-Scores

Normal Model

Standard Normal Model

The 68–95–99.7 Rule

The Normal Distribution

Types of Variables

Example Question

The Language of Variation: Variables

Representing Data with Charts

Frequency Table

Representing a Categorical Variable with Tables

Bar Graphs

Pie Charts

Contingency Table (Two-Way Table)

Representing a Categorical Variable with Graphs

Graphs

Histogram, Polygon and Ogive

Stem-and-Leaf Plot (Stemplot)

Dot-Plot

Representing a Quantitative Variable with Graphs

Describing Distributions

Shape

Center

Spread

Describing the Distribution of a Quantitative Variable

What Are Summary Statistics?

Statistics of Center

The Mean

The Median

Statistics of Spread

Standard Deviation

Summary Statistics for a Quantitative Variable

Graphical Representations of Summary Statistics 

5- Number Summary - Boxplot 

Graphical Representations of Summary Statistics

Comparing Groups with Histograms

Comparing Groups with Boxplots

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

Conditional Relative Frequency

Determining Associations from a Two-Way Table

Example

Statistics for Two Categorical Variables

What is a Scatterplot?❓

Describing Scatterplots🗒️

Form

Direction

Strength

Unusual Features

Representing the Relationship Between Two Quantitative Variables

What is Correlation?

Examples

Calculating the Correlation Coefficient

Correlation

What is a LSRL?

Extrapolation

Linear Regression Models

Residual Plots

Example 1

Example 2

Good or Bad? 🧐

Calculating Residuals

Residuals

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My Programs

Study with Hours

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Browse Subjects

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Upcoming College Deadlines

Bookmarks

4.8 Mean and Standard Deviation of Random Variables

Center of a Discrete Random Variable

Variability of a Discrete Random Variable

Resources:

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