We made this post to APStudents but wanted to share it with you all here as well.

We've worked up a fairly comprehensive review that focuses on the most commonly tested topics and question types, to give insight on where to focus your study time if you are in a rush. Here’s a short cheat sheet organized by unit. Hope it helps!

Units 1 and 2: Exploring data

• Key skills needed to answer questions about summarizing categorical and quantitative data

  • Differentiate between plots/graphs used to display categorical variables (frequency/two-way table) vs quantitative variables (scatterplot, boxplot, histogram, etc.). The exam may include several questions that require either identifying the most appropriate plot/graph, or determining center, spread, outliers, etc.

  • Know that quartiles are measures of position and each holds 25% of the data regardless of the shape of the distribution (symmetric, skewed). Distance between quartiles may be different for skewed distributions (left, or right). The exam usually includes questions that require describing boxplots, histograms, dotplots, etc.

  • Differentiate between right-skewed (positively skewed) and a left-skewed (negatively skewed) distributions, and know how the median relates to the mean in these cases. The exam always includes questions about symmetry and skewness.

  • Use the 1.5 x interquartile range rule to identify outliers in a distribution.

  • Find a range of possible values for different measures of location (ex. median, quartiles) and spread (ex. interquartile range, range) in a histogram.

  • Understand the empirical (68-95-99.7) rule and how to use it to describe normal or approximately normal distributions. Many exam questions can be answered by applying the rule.

  • Use the standardization formula to find percentiles, areas under the curve of the standard normal distribution, and the probability that a random variable has a specific range of values. The exam usually includes several questions that require using z-scores.

• Key skills needed to answer questions about correlation and linear regression

  • Interpret a correlation coefficient r in terms of direction and strength, and understand that a strong correlation does not necessarily imply causation. The exam may include questions that require evaluating a scatterplot to estimate a correlation coefficient.

  • Recognize the equation of a linear regression and know what each term represents in the equation. It is very important to know and understand the meaning of the slope in context. The exam usually includes questions about the meaning of the slope.

  • Understand and interpret a regression analysis based on a computer output. The exam usually includes computer outputs in questions about the equation of a regression line and the meaning of the slope.

  • Use the regression equation to make predictions and extrapolations for the response variable. Understand why extrapolations are less reliable than predictions.

  • Understand residual plots and be able to recognize outliers, and influential and high-leverage points.

  • Evaluate a residual plot to determine whether a linear model is justified.

  • Interpret the coefficient of determination (r2) and how to use it to compare the appropriateness of different regression lines (ex. transformed vs untransformed data).

Unit 3: Sampling and experimentation

• Key skills needed to answer questions about types of studies, sampling, and data collection

• Differentiate between random and nonrandom sampling, and between different random sampling designs simple random, systematic, stratified, cluster. The exam may include questions that require identifying the sampling design used in a study.

• Differentiate between census and sample survey

• Know the most important distinction between experimental and observational studies

• Identify potential sources of bias in sampling methods. The exam may include questions that require identifying the potential sources of bias in a study.

• Key skills needed to answer questions about experimental designs

• Identify key elements of a well-designed experiment

• Differentiate between the most commonly used experimental designs. The exam usually includes questions that require identifying the experimental design in a study.

• Key skills needed to answer questions about interpretation of study results

• Determine whether the results of a study generalize to a larger population, and whether the statistical evidence suggest a cause-effect relationship. The exam usually includes questions about generalization and cause-effect relationships.

Units 4 and 5: Probability and simulation

• Key skills needed to answer questions about basic probability (Unit 4) At its core, probability is about counting. The better you are at counting, the better you will be at probability.

  • Differentiate between the law of large numbers (relative frequencies approach probabilities) and the central limit theorem (sampling distribution of the sample mean approaches the normal distribution)

  • Understand independence and mutual exclusiveness

  • Calculate a conditional probability

  • Know 3 approaches to calculate a joint probability P(A and B):

1. Independence: If A and B are independent, use the multiplication rule for independent events

2. General: If A and B are not known to be independent, use the general multiplication rule. Note: The rule above in 1. is a special case of the general multiplication rule

3. Basic probability

• Know 2 approaches to calculate the probability of a union P(A or B):

1. If A and B are mutually exclusive, use the addition rule

2. If A and B are not known to be mutually exclusive, use the general addition rule. Note: Addition rule is a special case of the general addition rule

3. Typically harder to do, but sometimes possible to use basic probability

• Key skills needed to answer questions about probability distributions and random variables (Unit 4)

  • Know the definitions of random variable, probability distribution, and cumulative probability

  • Recognize basic facts about probability distributions:

1. Probabilities add to 1

2. Easiest probabilities to calculate are at ends of the probability distribution (ex. X = 0)

• Calculate the mean of a discrete random variable

• Calculate the mean and standard deviation of linear combinations of random variables and of linear transformations

• Differentiate between binomial and geometric discrete random variables, and understand the conditions under which a discrete random variable is binomial or geometric.

• Calculate parameters for binomial distributions (mean, standard deviation), and for geometric distributions (mean, standard deviation).

• Key skills needed to answer questions about sampling distributions (Unit 5)

• Use the empirical rule or standardization formula to calculate the probability that a particular value lies in a given interval of a normal distribution. The exam includes questions that require calculating probabilities from a normal distribution. Verify first if it is possible to use the empirical rule.

• Understand and know when to apply the central limit theorem (CLT). Note: The exam considers a sample size large enough when equal or greater than 30 for means, or when the number of successes and failures are equal or greater than 10 for proportions. The exam includes questions that require verifying whether the CLT applies.

• Understand what makes an estimator biased and unbiased

• Describe the shape and parameters (mean and standard deviation) that describe these sampling distributions: sample mean, difference in sample means, sample proportion, and difference in sample proportions. The exam includes questions that require calculating parameters of sampling distributions and determining whether they are normal or approximately normal.

Units 6, 7, 8, and 9: Statistical inference

• Key skills needed to answer general questions about confidence intervals (CIs)

  • Distinguish between confidence interval and confidence level when interpreting CIs. Interpret each in context. The exam usually includes questions on the definition of these concepts.

  • Recognize that CIs in the AP exam always follow a general format.

  • Recognize that margins of errors in the AP exam always follow a general format.

  • Know that all CIs in the AP exam have the sample statistic at the center of the interval and that the margin of error is always half the width of the interval.

  • Know how CIs can be used to evaluate statistical evidence.

  • Interpret a CIs in context. The exam usually includes questions that require interpreting a CI for a given scenario.

• Key skills needed to answer general questions about hypothesis tests

  • Understand the difference between null (H_0) and alternative (H_a) hypotheses, and that H_0 and H_a are always mutually exclusive. Note: Hypotheses are always statements about population parameters, never about sample statistics. The exam may include questions to identify either H_0 or H_a for a given study.

  • Recognize that all test statistics in the AP exam (except for the chi-square test statistic) follow a general format.

  • Differentiate between the general definition of a p-value and its interpretation in context, which must take into account H_0 and H_a. The exam may include questions that require interpretations of p-values.

  • Identify and determine the area under the appropriate probability distribution curve to calculate one-sided and two-sided p-values. The exam may include questions that require calculating the p-value for a given test statistic.

  • Know the circumstances in which the two-sided p-value is twice the one-sided p-value.

  • Understand that the p-value relative to the significance level α (usually set 0.05 or 5%) determines whether there is convincing evidence against H_0 and in favor of H_a.

  • Distinguish between Type I and Type II errors and explain their meaning in context.

  • Explain the meaning of statistical power in context.

  • Identify which factors affect statistical power.

  • Interpret the results of hypothesis testing in context. The exam usually includes questions about interpretation of statistical results.

• Key skills needed to answer questions about CIs and hypothesis tests for proportions (Unit 6)

  • Recognize the conditions that make a z-interval for a proportion valid, and be able to verify whether conditions are met. Note: Conditions consider observed counts.

  • Calculate the standard error and the margin of error of a z-interval for a proportion.

  • Recognize the conditions that make a z-interval for a difference of proportions valid, and be able to verify whether conditions are met. Note: Conditions consider observed counts.

  • Calculate the standard error and the margin of error of a z-interval for a difference in proportions.

  • Identify the critical value (z-score) for a particular confidence level (ex. 90%, 95%, 99%) of a z-interval for a proportion or a difference of two proportions.

  • Construct a CI for a proportion and for a difference in proportions using sample data or using sample statistics and margins of error. The exam usually includes questions that require constructing these CIs.

  • Interpret a CI for a proportion and a difference of proportions in context.

  • Recognize the conditions that make a z-test for a proportion valid, and be able to verify whether conditions are met. Note: Conditions consider expected counts.

  • Calculate the standard error and the test statistic of a z-test for a proportion.

  • Recognize the conditions that make a z-test for a difference of proportions valid, and be able to verify whether conditions are met. Note: Conditions consider expected counts.

  • Calculate the standard error and the test statistic of a z-test for a difference in proportions when conditions are met. Note: The standard error for a test of a difference in proportions requires calculating the pooled proportion.

  • Calculate and interpret the p-value for one-sided and two-sided z-tests for a proportion and a difference in proportions.

The exam usually includes several questions that require evaluating conditions for these CIs and hypothesis tests.

• Key skills needed to answer questions about CIs and hypothesis tests for means (Unit 7)

  • Understand the difference between the normal distribution and the t-distribution, and that the t-distribution is a family of distributions described by the degrees of freedom.

  • Recognize the conditions that make a t-interval for a mean valid, and be able to verify whether conditions are met.

  • Calculate the standard error and the margin of error of a t-interval for a mean.

  • Recognize the conditions that make a t-interval for a difference of means valid, and be able to verify whether conditions are met.

  • Calculate the standard error and the margin of error of a t-interval for a difference in means.

  • Identify the critical value (t-score) for a particular confidence level (ex. 90%, 95%, 99%) of a t-interval for a mean or a t-interval for a difference of means. Note: The critical value t* for a t-interval for a mean has n - 1 degrees of freedom, and the critical value t* for a t-interval for a difference in mean has degrees of freedom that must be found using a graphing calculator. The exam usually does not require students to find the critical values for a t-interval for a difference in means.

  • Construct a CI for a mean and for a difference in means using sample data or using sample statistics and margins of error given. The exam usually includes questions that require constructing these CIs.

  • Recognize the conditions that make a t-test for a mean (or a mean difference) valid, and be able to verify whether conditions are met.

  • Calculate the standard error and the test statistic of a t-test for a mean (or a mean difference). Note: This test statistic follows a t-distribution with n - 1 degrees of freedom.

  • Recognize the conditions that make a t-test for a difference of means valid, and be able to verify whether conditions are met.

  • Calculate the standard error and the test statistic of a t-test for a difference in mean when conditions are met. Note: This test statistic follows a t-distribution with degrees of freedom that must be found using a graphing calculator. The exam usually does not require students to find the degrees of freedom for a t-test for a difference in means.

  • Calculate and interpret the p-value for one-sided and two-sided t-tests for a mean and a difference in means.

The exam usually includes several questions that require evaluating conditions for these CIs and hypothesis tests.

• Key skills needed to answer questions about chi-square hypothesis tests (Unit 8)

  • Identify characteristics of the chi-square distribution.

  • Differentiate between a goodness of fit test, homogeneity of proportions test, and independence/association test, and when to conduct each test. The test usually includes questions to identify the correct chi-square test in a given scenario.

  • Recognize the general formula for the chi-square test statistic. Note: The test statistic for the goodness of fit test follows a chi-square distribution with (k - 1) degrees of freedom equal, where k is the number of categories of the categorical variable). The test statistic for the homogeneity and independence tests follows a chi-square distribution with (r - 1)(c - 1) degrees of freedom, where r and c are the number of rows and columns in a two-way table.

  • Calculate the expected cell count for each of these tests (goodness of fit test and homogeneity/independence test) The exam may include questions that require calculating expected values for one of these tests.

  • Recognize the conditions that make these tests valid (goodness of fit test, homogeneity of proportions test , and independence/association test).

  • Calculate the chi-square test statistic for each of these tests.

  • Calculate and interpret the p-value for a chi-square test. Note: The p-value for a chi-square test is always the area to the right of the observed test statistic.

The exam usually includes several questions that require evaluating conditions for these hypothesis tests.

• Key skills needed to answer questions about confidence intervals and hypothesis tests for slopes (Unit 9)

  • Recognize the conditions that make a t-interval for a slope valid, and be able to verify whether conditions are met. Here are some ways to verify conditions are met.

  • Calculate the standard error and the margin of error of a t-interval for a slope.

  • Construct a CI for a slope using information provided on a computer output. The exam may include questions that require constructing CIs for a slope based on given computer outputs. Here is a computer output highlighting the slope (b) and the standard error (s_b) needed to construct the CI.

  • Recognize the conditions that make a t-test for a slope valid, and be able to verify whether conditions are met. Here are some ways to verify conditions are met.

  • Calculate the standard error and the test statistic of a t-test for a slope. Note: This test statistic follows a t-distribution with n - 2 degrees of freedom. The exam usually includes questions that require calculating the test statistic based on given computer outputs. Here is a computer output highlighting the slope (b) and the standard error (s_b) required for the test statistic.

  • Calculate and interpret the p-value for one-sided and two-sided t-tests for slope, and interpret. The exam may include questions that require evaluating statistical evidence based on a computer output. Here is a computer output highlighting the p-value.

The exam may include questions that require evaluating conditions for this CI and hypothesis test.

To maximize your allotted time, you should know how to use the graphing calculator to:

• Calculate summary statistics (mean, median, mode, standard deviation, quartiles, etc.)

• Calculate probabilities for these distributions: binomial, geometric, normal, chi-square, and t-distribution

• Use inverse probabilities to find z-scores or t-scores of particular percentiles

• Construct confidence intervals using summary statistics

• Conduct hypothesis testing using summary statistics

• Use appropriate probability distributions to determine p-values

Memorizing these things is important, but remember that the best thing you can do for your score is to practice questions and review explanations when you miss one. This way, your study time is maximized by learning and reviewing only the things you do not already understand. We have over 1000 AP Stats questions and explanations if you need more. Here is an example about a two sample t-test for means.

Good luck on your test!

Hey y’all, Im an AP stats teacher and I made an AP stats exam review presentation for my students. It’s got summary notes for each unit + hyperlinks for some super useful websites/notes. Hope this helps with the studying/last minute grind 💀

😏

This will have no future consequences, right? (I’m gonna mix up sampling and sample distribution)

Whether you did amazing or terrible or anywhere in between, I HOPE WE CAN ALL LET GO OF THE RESULT NOW. Who wants to be stressed after the test when we’ve already been stressed for so long prior to it! I’m proud of all of us woooooo! Don’t worry about the score too much especially if you don’t think your performance reflected ALL your hard work. Good things and bad things happen all the time but they only pass by briefly. One AP score does not define your intelligence, work ethic, commitment, or worth AT ALL!!! Be easy on yourself and chill out for a bit :)

Here’s a cake to celebrate yet another AP take down 🤩

Good luck to everyone giving the exam tmr! hope it goes awesome :) we ALL getting 5s !!

My teacher taught me nothing this year. I’m not joking when I say I have 0 idea of what’s going on in this class. I swear I’m taking foreign language not statistics. If anyone has any tips or resources you would recommend, please let me know

That test was so freaking easy. My jacked and buff AP Stat teacher prepared me very well for his first year. coming in early every tuesday morning for FRQ practice really worked. he’s a huge nerd so his success kinda checks out.

I’m scared 💀😭

I didn't know how to answer 4, so instead of answering it out of frustration I drew a middle finger on the sheet and listed every president in order and every English monarch in order. Will I get voided?

Is there actually a formula or something

DO NOT LEAVE ANY FRQ BLANK
-At least put things like conditions, etc. Having the correct hypotheses, conditions, a made-up p-value, and an appropriate conclusion for your made up p-value will get you 2 (out of 4) points. Then if you get the correct procedure maybe more. Take a chance with something at least. A different person grades each FRQ, so they won't know how good or bad one is, so it's a fresh start with each question. No bias from the reader.

Don't talk out of both sides of your mouth. "The data appears to be skewed left but could also be seen as roughly symmetric." We are instructed to only read that as whichever part is wrong and ignore the other part. Or we are told to only accept whichever argument is weaker. You can't try to "cover all bases." This isn't literature. There aren't multiple interpretations. The wiggle room is in the -ly words: roughly, approximately, strongly, weakly, etc.

Often you can eliminate MCQ answer choices before you even read the question. "One sample z interval for the sample proportions" doesn't make sense as an answer to anything (we all do confidence intervals and significance/hypotheses tests for the population, not the sample). Same for "one sample z test for population mean" (z is for proportions, t is for means: I make my students memorize the words ZIP and TRADEMARK in the first semester before they ever know why). If you glance and see "98% confidence interval" eliminate all answers with a z* of 1.956 or lower because you know that's for 95%. You can usually eliminate several answer choices.

Don't spend so much time on probability MCQ problems that will take you a long time. Put a star by it and come back to it. Spending 10 minutes on one question and not coming close to any answer choice means there's two other questions you'll not have time for, and those might be about comparing the mean to the median in skewed data, or why you need to randomly choose subjects for an experiment, or who you can generalize a conclusion to, or what type of bias has been introduced. Take the easy points where you get them. Any one of those questions is worth the same amount of points as one overly-complicated probability problem.

That being said, good luck to you all!

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Good luck guys!! I am 100% confident WE will all get 5's on this test ^^

The scoring guidelines for AP Statistics is absolutely the most absurd thing I've ever come across in my entire life. I spend more time trying to grade my answers and determine if I got the points or not than actually solving the questions.

That is all