What Is (and Isnt) on the AP Statistics Formula Sheet

What Is (and Isn't) on the AP Statistics Formula Sheet SAT / ACT Prep Online Guides and Tips 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 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 is actually three 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 as well as below. The formula sheet has three sections, and each section takes up one page. Below are screenshots of the formula sheet, along with a list of the equations it includes (ordered from the top of the sheet to the bottom of the last page). Descriptive Statistics Formulas Sample mean Sample standard deviation Pooled sample standard error Simple linear regression line Regression coefficient Regression slope intercept Sample correlation coefficient Regression coefficient Standard error of regression slope Probability 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 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 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 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 ($Ã… ·$). It's used in regression analysis. Each data point has one residual. The formula looks like this: $\bi e \bo= \bi y \bo - \bi Ã… ·$ Both the sum of the residuals and the mean of the residuals are equal to zero, or $ÃŽ £ e = 0$ 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. Want to improve your SAT score by 160 points or your ACT score by 4 points? We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:

How Important Is Vocabulary for the New SAT

How Important Is Vocabulary for the New SAT SAT / ACT Prep Online Guides and Tips Studying hundreds of fancy words from big lists has long been a mainstay of SAT prep. But with the redesigned SAT focusing on medium-level words in the context of passages, do you still need to drill yourself on little-used vocab words? Before you expend superfluous energy to bolster your cognizance of recondite terminology (or waste time learning lots of obscure words), read this guide to learn whatvocabulary you need for the new SAT. First, what changes are being made to the SAT in terms of vocabulary? Changes in the New 2016 SAT The first and most apparent change in the redesigned SAT is the elimination of sentence completion questions. Gone are the stand-alone sentences with one or two blanks asking you to "choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole." Instead, the new vocabulary questions are passage-based. They refer to a line within a passage and ask what a word or idiom meansin context.This is a big difference from sentence completion-style questions, so what does this change mean in terms of the skills being tested? With sentence completions, you pretty much had to know the straight definition of complex wordsin order to answer them correctly. The sentence indicated a definition, so you either had to know which word it was referring to or be able to eliminate the other four answer choices. You couldn't rely on too many context clues to figure it out. This is where your studying of SAT Word of the Day and vocabulary lists would kick in and help you fill in the blanks. With the new passage-based questions, you're asked to interpret the meaning of a medium-level word in context. The word may be familiar to you, but it can have different meanings or connotations depending on how it's used. On these types of questions, all of the answers may be correct as definitions of the term being considered. Only one answer choice, though, will be correct for the term as it's being used in that particular context. As you can tell, this is a big departure from sentence completions. It calls upon different skills and a different approach to studying vocabulary. Before discussing how you can adjust your test prep, let's look at a couple examples that illustrate these changes. Does all this change make cents? Old SAT Vocabulary Questions The old SAT had 19 sentence completion questions which tested traditional SAT vocabulary terms. The following is a typical example. There is no doubt that Larry is a genuine -: he excels at telling stories that fascinate his listeners. (A) braggart(B) dilettante(C)pilferer(D) prevaricator(E) raconteur This sentence indicates the definition of the vocabulary word: a person who excels at telling fascinating stories. You either have to know that "raconteur" means just that, or you have to know thatthe other choices don't fit that definition and use process of elimination to get to (E). If you don't know these words and their definitions, you're left having to make a wild guess. The new SAT, on the other hand, usually doesn't feature such difficult words. Let's take a look. Redesigned SAT Vocabulary Questions The new SAT asks about words as they occur within the context of the passage. You probably don't use "prevaricator" and "raconteur" all that often in daily conversation. The words on the new SAT are meant to have broader utility in college and professional life. According to College Board, the new SAT emphasizes "the meaning of words in extended contexts and on how word choice shapes meaning, tone, and impact." They give the following example (this is an excerpt from a longer passage): "...The coming decades will likely see more intense clustering of jobs, innovation, and productivity in a smaller number of bigger cities and city-regions. Some regions could end up bloated beyond the capacity of their infrastructure, while others struggle, their promise stymied by inadequate human or other resources." As used in line 55, "intense" most nearly means... (A) emotional(B) concentrated(C) brilliant(D) determined Based on this example, you can immediately see the difference in the vocabulary's level of difficulty. You can also see how all of those answer choices could be correct interpretations of "intense"- depending on its context, it could mean emotional, concentrated, brilliant, or determined. Only (B) concentrated, however, works within this passage, as intense is being used to describe the "clustering of jobs...in a smaller number of bigger cities and city-regions." Rather than calling upon your knowledge of a word's definition, this question asks you to glean meaning and connotation from the context of a passage. Did you notice any other differences in this question? It only has four answer choices, instead of five. These improved odds, plus the fact that the new SAT has no penalty for wrong answers, means you should always make your most informed guess on all the questions. Some other medium-level difficulty words that might be tested on the new SAT include "alleviate, consistent, synthesis, empirical, coincide, congenial, indelible, discord, occur, mention, emerge, admit, perform, fortunate, require, and maintain." Even if you think you know all these words, is there a way you can study them to be better prepared for SAT vocab questions? What Do These Changes Mean for Your Studying? Given these changes, do you still need to study vocabulary for the new SAT in 2016? I would still highly recommend studying vocabulary, but in a different way. You can forget about those lists of "2,000 SAT vocabulary words" (phew!) and focus on "multiple-meaning" words of medium-level difficulty. The key thing to remember is that these words might have different meanings in different contexts, so you want to ensure that you understand each word in all of its dimensions and applications. You can do this by finding a word used in several example sentences, rather than just one, as well as noting how vocabulary words are used when you readbooks, articles, and the news. The New York Times Word of the Day Learning Blog has a useful tool that lets you find all the articles in which a term shows up. While many of the words they feature apply better to the old SAT, you can use that idea of finding terms in many different sources to enhance your understanding of it. There are also several other sites that are helpful for studying these words in various contexts, like Quizlet and ProfessorWord. Plus, incorporating them into your own writing is the best way to fully grasp how their meaning is affected by word choice and usage. Since these changes closely resemble the ACT, you can also check PrepScholar's list of the 150 most commonly tested ACT words. College Board and Khan Academy have sample practice questions for the new SAT. Finally, when using older practice materials, I would recommend focusing on the passage-based questions, especially the ones that point to a specific word or phrase. Generally speaking, you can forget about the sentence completions. Overall, what are the most important takeaways from the changes that were made to the SAT? The Gist of Vocabulary Changes The following are the most important points to remember about vocabulary questions on the new SAT: Sentence completions are gone. New questions focus on moderate-level words that may have different meanings in different contexts, like "intense." To prepare, you should focus on learning how words are used in different contexts, along with how you can gather context clues to determine the meaning of a word. Check out sample questions for the new SAT and make sure you understand the changes that are being made. This will help you adjust your studying and not waste time focusing on material that's no longer relevant. Plus, studying vocabulary based on context will help you improve your overall writing, reading, and communication skills, which will be extremely helpful for high school, college, and beyond. What's Next? Besides vocabulary questions, what else is changed on the new SAT? Read about all the changes and what it means for your test prep in our full guide to the redesigned SAT in 2016. In addition to learning about the changes, figure out what these changes mean for your studying. Read all about how to study for the new SAT here. Want to improve your SAT score by 160 points?We've written a guide about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now: