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📆Big Reviews: Finals & Exam Prep

15 min read•march 9, 2021

We know that studying for your AP exams can be stressful, but Fiveable has your back! We have created a study plan that will help you crush your statistics exam. We will continue to update this guide with more information about the 2021 exams, as well as helpful resources to help you score that 5. __Create a Fiveable account__ and __join our Discord__ to stay involved in all things AP exams! 😁

This year, all AP exams will cover all units and essay types. The 2021 Statistics exam format will be:

Section 1: Multiple Choice - 50% of your score

- 40 questions in 1 hr 30 mins

Section 2: Free Response - 50% of your score

- 6 questions in 1 hr 30 mins

**Part A:**- 1 multipart question with a focus on collecting data
- 1 multipart question with a focus on exploring data
- 1 multipart question with a focus on probability and sampling distributions
- 1 multipart question with a focus on inference
- 1 multipart question that combines 2 or more skill categories

**Part B:**- 1 investigative task that assesses multiple skill categories and content areas

Section 1: Multiple Choice - 50% of your score

- 40 questions in 1 hr 30 mins

Section 2: *Multiple Choice and *Free Response - 50% of your score

- 11 multiple choice questions in 25 minutes
- 4 free-response questions in 1 hour and 5 minutes
**Part A:**- 1 multipart question with a primary focus on collecting data
- 1 multipart question with a primary focus on exploring data
- 1 question that combines 2 or more skill categories

**Part B:**- 1 investigative task that assesses multiple skill categories and content areas

Check out our study plan below to find resources and tools to prepare for your AP Statistics exam.

There are three different exam administrations this year and the tests will be taken in person at your school unless your AP Coordinator has indicated otherwise. Here is what we know from College Board so far:

**The first administration offers the exam on paper, in school, on Monday, May 17, 2021, at 12 PM, your local time.****The second administration offers the exam on paper, in school, on Tuesday, May 25, 2021, at 12 PM, your local time.****The third administration offers the exam digitally, in school and at home, on Thursday, June 10, 2021, at 4 PM EDT.**

You will have 3 hours to take the exam. __Create a Fiveable account__ to get updates on the latest 2021 exam news.

Before we begin, take some time to get organized. Remote learning can be great, but it also means you’ll need to hold yourself accountable more than usual.

**🖥 Create a study space.**

Make sure you have a designated place at home to study. Somewhere you can keep all of your materials, where you can focus on learning, and where you are comfortable. Spend some time prepping the space with everything you need and you can even let others in the family know that this is your study space.

**📚 Organize your study materials.**

Get your notebook, textbook, prep books, or whatever other physical materials you have. Also create a space for you to keep track of review. Start a new section in your notebook to take notes or start a Google Doc to keep track of your notes. Get yourself set up!

**📅 Plan designated times for studying.**

The hardest part about studying from home is sticking to a routine. Decide on one hour every day that you can dedicate to studying. This can be any time of the day, whatever works best for you. Set a timer on your phone for that time and really try to stick to it. The routine will help you stay on track.

**🏆 Decide on an accountability plan.**

How will you hold yourself accountable to this study plan? You may or may not have a teacher or rules set up to help you stay on track, so you need to set some for yourself. First, set your goal. This could be studying for x number of hours or getting through a unit. Then, create a reward for yourself. If you reach your goal, then x. This will help stay focused!

**🤝 Get support from your peers.**

There are thousands of students all over the world who are preparing for their AP exams just like you! Join our __Discord channel__ to chat, ask questions, and meet other students who are also studying for the spring exams. You can even build study groups and review material together!

**Big takeaways:**

Unit 1 is about creating and analyzing graphs of data. This includes both categorical and quantitative data. For categorical data, we should be able to read and create tables and bar graphs and calculate proportions/percentages. For quantitative data, we should be able to read and create dot plots, stemplots, histograms, and boxplots. We should also be able to describe the shape, center, variability (spread), and any unusual features of a distribution of quantitative data. This includes making calculations such as mean, median, range, interquartile range (IQR), and standard deviation. Our descriptions and calculations can be used to compare data from multiple groups. Finally, Unit 1 ends with describing the position of individuals within a quantitative data set, including using percentiles and z-scores. This leads us to an initial exploration of the Normal Distribution, though we will study that more in-depth in Units 4-5.

**Definitely do this:**

- 🎥
**Watch these videos from the Fiveable archives:****Analyzing Categorical Variables**: An intro to some key terms and graphs (use first 15 minutes)**Graphing & Analyzing Quantitative Variables**: The types of graphs you need to know!**Describing Data in a Distribution**: A breakdown of percentile a cumulative graphs**Normal Distributions**: A good intro to all things Normal!

- 📰
**Check out these articles:**: A real-life example of how z-scores can help compare individuals from different distributions, using golfers (source: Grantland)__Relative Dominance__

- ✍️
**Practice**:: check out this post and practice your free-response skills!**Practice an AP-Style Problem**

**If you have more time or want to dig deeper:**

**💎 Check out some online applets:**: Play with this applet to get a sense of how changing different data values impacts the mean and median__Mean vs. Median interactive applet__: A visual of the Standard Normal Curve. Update the mean and standard deviation to look at any data set.__Normal Distribution applet__

**Big takeaways:**

Unit 2 is about creating and analyzing graphs of data when two variables are measured about each individual in a data set. For categorical data, we should be able to read and create two-way tables or segmented bar graphs and calculate conditional percentages. These can be used to comment on the association (or lack thereof) between the two variables. For quantitative data, we should be able to read, create, and describe scatterplots, which can also be used to comment on the apparent association between two variables.

The second half of Unit 2 is then focused on linear regression, a process by which we can make predictions about one quantitative variable (a response variable) using another (an explanatory variable). We should be able to use Least-Squares Regression Lines to make these predictions, and interpret several components of the LSRLs (including slope, intercept, and other calculated values such as s or r2)

**Definitely do this:**

**🎥 Watch these videos from the Fiveable archives:****Analyzing Categorical Variables**: Start at 14:38 for an example of two-way tables and stay for segmented bar graphs**Describing Scatterplots & Association**: How to describe the direction, strength, and form of an association, as well as an introduction to the correlation coefficient*r***Using Least-Squares Regression Lines**: How to make predictions from regression lines and calculating residuals**Advanced Linear Regression**: Interpreting “s”, “r2”, and reading computer outputs of regression data

- ✍️
**Practice**:: check out this post and practice your free-response skills!**Practice an AP-Style Problem**

**If you have more time or want to dig deeper:**

- 🌶 Join the live cram stream for unit 2. Get your cram pass now.
**💎 Check out some online applets:**: Try to guess the least-squares regression line from a scatterplot of data__Least-Squares Regression__

**😀 Just for fun!**: Data sets with very high “r” values that… well… you’ll see... [Source: Tyler Vigen]__Spurious Correlations__

**Big takeaways:**

While Units 1-2 were about graphing and analyzing sets of data, Unit 3 is about examining the methods through which we can collect that data. For sample surveys, we should be able to describe various methods of selecting samples, particularly the random methods (simple random, stratified random, cluster, and systematic samples). However, not all samples are collected through a random process, and we should be prepared to discuss possible sources of bias in surveys (including via non-random selection processes).

We then turn to the differences between observational studies and experiments, and the features of a well-designed experiment. We should be able to define many common terms associated with experiments (many of which you’ve likely seen in other courses!), and compare and contrast several common experimental designs: completely randomized design, randomized block design, and matched-pairs design.

**Definitely do this:**

**🎥 Watch these videos from the Fiveable archives:****Sampling Methods and Sources of Bias**: A breakdown of the different ways we can take samples, and how to talk about bias on the AP exam.**Experiments and Observational Studies**: All things experiments! Includes a discussion of the possible pitfalls of observational studies (confounding)

- ✍️
**Practice**:: a practice question on surveys and sampling methods.**AP-Style Problem #1**: a practice question on observational studies/experiments__AP-Style Problem #2__

**Big takeaways:**

Unit 4 is where AP Statistics gets “math-y,” with lots of calculations and formulas. We are asked to calculate or interpret probabilities in a variety of settings, beginning with the understanding that probability reflects what we should expect to occur over the long run. We should be able to design and execute simulations for a given scenario - and then the calculations begin. We should be able to calculate the probability of multiple events using a variety of strategies (including Two-Way Tables, Tree Diagrams, and/or Venn Diagrams).

We should also be able to categorize different events as “mutually exclusive” or “independent,” with justification. Conditional probability [P(A | B)] plays a big role in this part of the unit. Shifting over to random variables, we should be able to calculate the mean (expected value) or standard deviation of a random variable, and combine them using similar rules to Unit 1. We conclude Unit 4 with a look at Binomial and Geometric random variables, which are two special types of variables that arise frequently in applications.

**Definitely do this:**

- 🎥
**Watch these videos from the Fiveable archives:****Randomness & Simulation**: Explore some definitions (and myths) about probability and randomness**Basic Probability Rules**: A breakdown of commonly-tested probability rules, using Two-Way Tables for most scenarios**Random Variables & Binomial/Geometric Distributions**: A summary of Random Variable facts & formulas

- 📰
**Check out these articles:**: An exploration of the misuse of probability rules in court cases [source: Significance Magazine]**Statistics in Court: Incorrect Probabilities**

**✍️ Practice:**: Some basic probability calculations using a discrete random variable__Practice FRQ #1__: Test your knowledge of binomial scenarios and simulations**Practice FRQ #2**: A scenario involving a two-way table**Practice FRQ #3**

**If you have more time or want to dig deeper:**

- 💎
**Check out some online applets:**: Play with this applet to get a sense of how probability works over the “long run”__Dice & The Law of Large Numbers__: A similar applet using coin flips__Coin Flips__

**Big takeaways:**

Unit 5 provides the bridge from descriptive statistics (Units 1-4) to inferential statistics (Units 6-9). After reviewing the Normal Distribution and introducing the idea of using sample statistics (like p or x) to estimate population parameters, we explore the creation of sampling distributions.

We meet the conditions for inference: **random** samples, **large** samples (for categorical variables, we need at least 10 expected successes and failures; for quantitative variables, we need n to be at least 30), and **independent** observations (which turns into the “10% rule” for sampling without replacement: if the sample size n is less than 10% of the population size N, we can do calculations as if we sampled with replacement).

If these conditions are met, the sampling distribution we build will be approximately Normal and all of our formulas for calculating the mean and standard deviation of sampling distributions on the formula sheet will hold. We then build sampling distributions for sample proportions/sample means and the difference of sample proportions/sample means.

**Definitely do this:**

**🎥 Watch these videos from the Fiveable archives:****Sampling Distributions for Proportions**: an intro to vocabulary surrounding sampling distributions, and a simulation using a virtual “candy machine”**Sampling Distributions for Means**: an intro to the building of a sampling distribution for x-bar and a summary of the Central Limit Theorem

**✍️ Practice:**: describe a sampling distribution and compute an associated probability__Unit 5 Practice FRQ__

**If you have more time or want to dig deeper:**

- 💎
**Check out some online applets:**: Build a sampling distribution for p-hat.__The "Candy Machine"__: See the Central Limit Theorem in action! Definitely try to make a “custom” graph to give the population a unique shape.**Sampling Distribution for x-bar**

**Big takeaways:**

Unit 6 is where we meet Confidence Intervals and Hypothesis Tests for the first time, specifically z-intervals and z-tests for population proportions. After learning “the basics” about confidence intervals (what’s a confidence level? What’s a margin of error?), we construct and interpret 1 and 2-sample z-intervals.

These intervals, built from samples, can be used to justify claims about a population. Then, after exploring the rationale behind hypothesis tests (including how to write null/alternative hypotheses and interpret a p-value in context), we run 1 and 2-sample z-tests. Finally, we meet “Errors”: both Type I (rejecting a true H0) and Type II (failing to reject a false H0), and define the “Power” of a test as the probability of correctly rejecting a false H0. This unit is often heavily tested and is well worth your time to review!

**Definitely do this:**

**🎥 Watch these videos from the Fiveable archives:****Confidence intervals for p**: An intro to Confidence Intervals and a breakdown of how to construct and interpret 1-sample z-intervals.**Hypothesis Tests for p**: An intro to Hypothesis Tests and practice running 1 and 2-sample z-tests.**Errors & Power of a Test**: A breakdown of the types of errors in hypothesis testing, and how to increase the power of a test.

**📰 Check out these articles:**: A breakdown of the Types of Errors with “boy who cried wolf” examples [Source: William Schmarzo]**Understanding Type I and Type II Errors**

**✍️ Practice:**: Test your knowledge about Confidence Intervals!**Unit 6 Practice FRQ #1**: “Convincing Statistical Evidence that…”__Unit 6 Practice FRQ #2__

**If you have more time or want to dig deeper:**

- 💎
**Check out some online applets:**: play with the population parameters and see what we mean by “confidence level”**Confidence Intervals for p**: demonstrates the idea of Hypothesis Testing using basketball free-throws.**Reasoning of a Hypothesis Test**

**Big takeaways:**

Unit 7 is an extension of Unit 6: we basically do everything again, but with t-procedures instead of z-procedures! We build Confidence Intervals and run Hypothesis Tests for a population mean or a difference of population means.

For the difference of population means, we must be able to distinguish between if we are running a 2-sample procedure or a matched-pairs procedure (in which we will use a 1-sample procedure to execute the process).

**Definitely do this:**

- 🎥
**Watch these videos from the Fiveable archives:****Confidence Intervals for Mu**: An refresher on Confidence Intervals and a breakdown of the t-distribution**Hypothesis Tests for Mu**: Lots of good FRQ practice**Errors & Power of a Test**: A breakdown of the types of errors in hypothesis testing, and how to increase the power of a test. (same as from Unit 6)**Review of z and t procedures**: A (mostly) comprehensive review of Units 6 and 7. Great for last-minute preparations!

- ✍️
**Practice**:: should we shut down the production line?**Unit 7 Practice FRQ #1**: which type of test should we run?**Unit 7 Practice FRQ #2**

**If you have more time or want to dig deeper:**

- 💎
**Check out some online applets:**: play with the population parameters and see what we mean by “confidence level”__Confidence Intervals for Mu__: Explore how the “Power” of a test is impacted by various inputs**Statistical Power**

**Big takeaways:**

Unit 8 is where we learn about chi-square tests, which can be used when there are two or more categorical variables. We’ll learn how to select from the following tests: the chi-square test for goodness of fit (for a distribution of proportions of one categorical variable in a population), the chi-square test for independence (for associations between categorical variables within a single population), or the chi-square test for homogeneity (for comparing distributions of a categorical variable across populations or treatments).

**Definitely do this:**

**🎥 Watch these videos:****📰 Check out these articles:****✍️ Practice:**

**If you have more time or want to dig deeper:**

- 💎
**Check out some online applets:**

**Big takeaways:**

Unit 9 will teach students how to construct confidence intervals for and perform significance tests about the slope of a population regression line when appropriate conditions are met. Surprisingly, there is variability in slope, which differs from students’ experience in previous courses. Slopes will likely vary as part of an approximately normal sampling distribution centered at the (true) slope of the population regression line relating spring length to hanging mass.

**Definitely do this:**

- 🎥
**Watch these videos:** - ✍️
**Practice**:

**If you have more time or want to dig deeper:**

- 💎
**Check out some online applets:**

Browse Study Guides By Unit

📆Big Reviews: Finals & Exam Prep

2021 AP Statistics Exam Guide

- 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)

✏️Blogs

✍️Free Response Questions (FRQs)

👆Unit 1: Exploring One-Variable Data

✌️Unit 2: Exploring Two-Variable Data

🔎Unit 3: Collecting Data

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

📊Unit 5: Sampling Distributions

⚖️Unit 6: Inference for Categorical Data: Proportions

😼Unit 7: Inference for Qualitative Data: Means

✳️Unit 8: Inference for Categorical Data: Chi-Square

📈Unit 9: Inference for Quantitative Data: Slopes

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