If you're going to be taking the AP Statistics exam, you're in luck! During the test, you'll have access to a formula sheet that has many useful equations. However, you need to know exactly what's on the AP Statistics formula sheet and how to use it before test day in order for it to be helpful.
In this guide, we go over everything you need to know about the newly-updated AP Stats formula sheet. We'll explain the exact equations that it includes, show you what the formula sheet looks like, go over a few important equations it doesn't contain, and give you tips on how to get the most out of it.
What's on the AP Statistics Formula Sheet?
The AP Stats formula sheet was updated in 2019 to better meet the needs of students during the exam. It's actually two pages of statistics formulas that you'll be given on test day. The formulas will be at the beginning of both the multiple-choice and free-response sections of the test, so you'll have access to them for the entire AP exam. That's great because that means you don't need to memorize any of these formulas!
What's on this AP statistics cheat sheet? You can see exactly what the formula sheet will look like here (beginning on page 261) as well as below.
The formula sheet has three sections: descriptive statistics, probability and distributions, and sampling distributions and inferential statistics. Below are screenshots of the formula sheet, along with a list of the equations it includes.
Descriptive Statistics Formulas
- Sample mean
- Sample standard deviation
- Simple linear regression line
- Regression coefficient
- Sample correlation coefficient
- Regression coefficient
Probability and Distributions Formulas
- Rule of addition
- Rule of multiplication
- Expected value of $X$
- Variance of $X$
- Binomial formula
- Mean of binomial distribution
- Standard deviation of binomial distribution
- Mean of geometric distribution
- Standard deviation of geometric distribution
Sampling Distributions and Inferential Statistics Formulas
- Standardized test statistic
- Confidence interval
- Standard deviation of sample mean
- Standard deviation of proportion
- Standard deviation of difference of sample means
- Standard deviation of difference of sample proportions
- Chi-square test statistic
- Standard error of regression slope
- Mean of sampling distribution of the proportion
- Standard deviation of sampling distribution of the proportion
- Mean of sampling distribution of the mean
- Standard deviation of the sampling distribution of the mean
- Sampling distribution of a sample slope
What Isn't on the AP Statistics Reference Sheet That You Should Know?
The AP Statistics formula sheet contains pretty much all the equations you need to know for the exam, but there are some equations they've left out that may come in handy on test day. Below are the most important of these. Be sure to memorize them because they won't be listed on the AP Stats formula sheet!
Descriptive Statistics
Interquartile Range
The interquartile range, or IQR, is the middle 50% of values when ordered from lowest to highest. The IQR is the difference between the 75th and 25th percentiles, or the first quartile subtracted from the third quartile. The IQR is used to show dispersion, and it can be a useful way to describe the data in boxplots, histograms, scatterplots, etc.
The equation is IQR = Q3-Q1
You can also use IQR to determine if an outlier exists. A commonly used formula is if a data point is more than $\bo 1.5*$IQR above Q3 or below Q1, then it's an outlier.
Residuals
The residual ($e$) is the difference between the observed value of the dependent variable (y) and the predicted value ($ŷ$). It's used in regression analysis. Each data point has one residual.
The formula looks like this: $e=y−ŷ$
Both the sum of the residuals and the mean of the residuals are equal to zero, or $Σe=0$ and $e=0$.
Probability
Bayes' Theorem
Bayes' theorem is useful for calculating conditional probabilities. You'll use conditional probability when trying to find the probability of an event given that another event has already occurred.
Conditional probability questions usually follow a format similar to "Given $x$, what is the probability that $y$ occurs?" Use Bayes' theorem to solve them.
Bayes' Theorem: $P(A|B)={P(B|A)*P(A)}/{P(B)}$
Tips for Getting the Most out of the AP Stats Formula Sheet
As you can see, the AP Statistics formula sheet can be very useful during the exam since it helps you avoid memorizing long lists of equations. There are some tips to getting the most out of it though, and we go over the three most important in this section.
#1: Know How to Use the Formulas
It seems like obvious advice, but it's very easy to take a glance at the AP Statistics cheat sheet and move on, knowing you'll have it with you on the test. However, test day is not when you want to be trying to understand what the different formulas mean or how to use them.
If you go into the AP exam not sure of what's on the formula sheet, you'll lose tons of valuable time searching for the right equations and struggling with how to use them properly.
Well before exam day, be sure to go through every formula on the sheet and make sure you understand it and know how to use it.
The College Board includes each of these formulas because they think they're necessary for doing well on the AP Statistics exam, so you should trust them and make sure you know them! If you're not sure how to use some of the equations, here's a helpful site that goes over what each of the formulas is used for.
#2: Know Calculator Shortcuts
You're allowed a graphing calculator for the entire exam, and you should take advantage of some of the nifty things it does. Calculator shortcuts can save you precious time on the test by quickly solving certain AP Statistics equations and finding pieces of data. They also give you a way to check your work for some problems. Stanford has a handy list of calculator shortcuts you can use with your graphing calculator.
There are two caveats though. First, don't become so dependent on your calculator that you forget how to solve the equations on your own or the logic behind them. Second, you should use calculator shortcuts primarily for the multiple-choice section of the test, where you just have to select the correct answer choice.
For the free-response section of the exam, you'll need to show all the work you did for each question, and simply writing which shortcut you plugged into your calculator won't cut it. Use the shortcuts primarily to check your work on free response.
#3: Take Practice Tests With the Formula Sheet
Answering practice questions and taking practice tests using the AP Statistics formula sheet is also key to doing well on the exam. You should take several practice AP tests before the actual exam, and for each of them you should use the official AP Statistics formula sheet. Your teacher will also likely give you a copy of the formula sheet for your in-class exams, so you can get some practice in there too.
If you need help finding practice tests, check out our guide specifically on where to find the best AP Statistics practice questions and tests.
Summary: Using the AP Statistics Formula Sheet
The AP Statistics reference sheet can be a big help during the exam, but only if you already know what's on it and how to use it. The formula sheet is actually three pages that contain useful equations in descriptive statistics, probability, and inferential statistics.
While this AP Statistics cheat sheet doesn't contain everything you need to know, it does include many key AP Statistics equations that you'll need to use on the test.
In order to get the most out of your AP Stats formula sheet, make sure you know all the formulas, pick up some useful calculator shortcuts, and be sure to take some practice tests with the AP Statistics reference sheet.
What's Next?
Looking for more AP Statistics prep? Check out our ultimate guide to the AP Statistics exam to learn everything you need to know to ace the test.
How's your grasp on calculating significance? Brush up on your t-tests and how to calculate statistical significance here.
Practice tests are key to preparing for AP Statistics. Our guide has links to all the best AP Stats practice tests so you can put your formula sheet to use!
How many AP classes should you take? Get your answer based on your interests and your college goals.
