The Ultimate Guide to the AP Statistics Exam

The Ultimate Guide to the AP Statistics Exam SAT / ACT Prep Online Guides and Tips Are you taking AP Statistics? If so, you're likely wondering what to expect from the AP Statistics exam. Before you sit down to take the final test, it's important to understand how the AP Stats test is formatted, what topics it will cover, and how it'll be scored. This guide will explain all of that information, show you official sample problems and give you tips on the best way to prepare for the AP Statistics test. In 2020, the AP Statistics exam will take place on Friday, May 15th at 12:00pm. How Is the AP Statistics Exam Structured? How long is the AP Statistics exam? The test is a total of three hours long and contains two sections: multiple choice and free response. You're allowed a graphing calculator for the entire exam. Multiple-Choice Section 40 multiple-choice questions 90 minutes long Worth 50% of exam score You can spend an average of a little more than two minutes on each multiple-choice question and finish the section in time. Free-Response Section 5 short-answer questions 1 Investigative Task 90 minutes long Worth 50% of exam score The five short-answer questions are meant to each be solved in about 12 minutes, and the Investigative Task is meant to be solved in about 30 minutes. What Does the AP Statistics Exam Test You On? The content of the AP Stats exam and course is centered around four major topics. Below are the four topics, along with what percentage of the exam will be on them and all the topics that fall beneath each of them. The list covers every single topic that the AP Statistics exam could test you on. #1: Exploring Data: Describing Patterns and Departures From Patterns (20-30%) Constructing and interpreting graphical displays of distributions of univariate data (dotplot, stemplot, histogram, cumulative frequency plot) Center and spread Clusters and gaps Outliers and other unusual features Shape Summarizing distributions of univariate data Measuring center: median, mean Measuring spread: range, interquartile range, standard deviation Measuring position: quartiles, percentiles, standardized scores (z-scores) Using boxplots The effect of changing units on summary measures Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) Comparing center and spread: within group, between group variation Comparing clusters and gaps Comparing outliers and other unusual features Comparing shapes Exploring bivariate data Analyzing patterns in scatterplots Correlation and linearity Least-squares regression line Residual plots, outliers, and influential points Transformations to achieve linearity: logarithmic and power transformations Exploring categorical data Frequency tables and bar charts Marginal and joint frequencies for two-way tables Conditional relative frequencies and association Comparing distributions using bar charts #2: Sampling and Experimentation: Planning and Conducting a Study (10-15%) Planning and conducting experiments Characteristics of a well-designed and well-conducted experiment Treatments, control groups, experimental units, random assignments and replication Sources of bias and confounding, including placebo effect and blinding Completely randomized design Randomized block design, including matched pairs design Overview of methods of data collection Census Sample survey Experiment Observational study Planning and conducting surveys Characteristics of a well-designed and well-conducted survey Populations, samples, and random selection Sources of bias in sampling and surveys Sampling methods, including simple random sampling, stratified random sampling, and cluster sampling Generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys #3: Anticipating Patterns: Exploring Random Phenomena Using Probability and Simulation (20-30%) The normal distribution Properties of the normal distribution Using tables of the normal distribution The normal distribution as a model for measurements Probability Interpreting probability, including long-run relative frequency interpretation "Law of Large Numbers" concept Addition rule, multiplication rule, conditional probability, and independence Discrete random variables and their probability distributions, including binomial and geometric Simulation of random behavior and probability distributions Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable Combining independent random variables Notion of independence versus dependence Mean and standard deviation for sums and differences of independent random variables Sampling distributions Sampling distribution of a sample proportion Sampling distribution of a sample mean Central Limit Theorem Sampling distribution of a difference between two independent sample proportions Sampling distribution of a difference between two independent sample means Simulation of sampling distributions t-distribution Chi-square distribution #4: Statistical Inference: Estimating Population Parameters and Testing Hypotheses (30-40%) Estimation (point estimators and confidence intervals) Estimating population parameters and margins of error Properties of point estimators, including unbiasedness and variability Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals Large sample confidence interval for a proportion Large sample confidence interval for a difference between two proportions Confidence interval for a mean Confidence interval for a difference between two means (unpaired and paired) Confidence interval for the slope of a least-squares regression line Tests of Significance Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power Large sample test for a proportion Large sample test for a difference between two proportions Test for a mean Test for a difference between two means (unpaired and paired) Chi-square test for goodness of fit, homogeneity of proportions, and independence (one- and two-way tables) Test for the slope of a least-squares regression line AP Statistics Sample Questions As we mentioned above, there are three types of questions on the AP Stats exam: multiple choice, short answer, and investigative task. Below are examples of each question type. You can see more sample questions and answer explanations in the AP Statistics Course Description. Multiple-Choice Sample Question There are 40 multiple-choice questions on the exam. Each has five answer options. Some questions will be accompanied by a chart or graph you need to analyze to answer the question. Short-Answer Sample Question There are five short-answer questions on the AP Stats test. Each of these questions typically includes several different parts you need to answer. You're expected to spend about 12 minutes on each short-answer question. Investigative Task Sample Question The final question on the exam is the Investigative Task question. This is the most in-depth question on the test, and you should spend about 30 minutes answering it. It will have multiple parts you need to answer and require multiple statistics skills. You'll also need to provide a detailed explanation of your answers that shows the strength of your statistics skills. Be sure to show all your work as you'll be graded on the completeness of your answer. How Is the AP Statistics Test Graded? For the multiple-choice part of the exam, you earn one point for each question you answer correctly. There are no point deductions for incorrect answers or questions you leave blank. Official AP graders will grade your free-response questions. Each of the six free-response questions is scored on a scale of 0 to 4 points, so the total section is out of 24 points. The free-response questions are graded holistically, which means, instead of getting a point or half a point for each bit of correct information you include, graders look at your answer to each question as a "complete package," and your grade is awarded on the overall quality of your answer. The grading rubric for each free-response question is: 4: Complete Response: Shows complete understanding of the problem's statistical components 3: Substantial Response: May include arithmetic errors, but answers are still reasonable and show substantial understanding of the problem's statistical components 2: Developing Response: May include errors that result in some unreasonable answers, but shows some understanding of the problem's statistical components 1: Minimal Response: Misuses or fails to use appropriate statistical techniques and shows only a limited understanding of statistical components by failing to identify important components 0: No Response: Shows little or no understanding of statistical components What does holistic grading mean for you? Basically, you can't expect to earn many points by including a few correct equations or arithmetic answers if you're missing key statistical analysis. You need to show you understand how to use stats to get a good score on these questions. Estimating Your AP Statistics Score If you take a practice AP Stats exam (which you should!) you'll want to get an estimate of what your score on it is so you can get an idea of how well you'd do on the real exam. To estimate your score, you'll need to do a few calculations. 1. Multiply the number of points you got on the multiple-choice section by 1.25 2. For free-response questions 1 through 5, add the number of points you got together and multiply that sum by 1.875 (don't round). If you need help estimating your score, the official free-response questions we linked to above include sample responses to help you get an idea of the score you'd get for each question. 3. For free-response question #6, multiply your score by 3.125. 4. Add the scores you got in steps 1-3 together to get your Composite Score. For example, say you got 30 questions correct on the multiple-choice section, 13 points on questions 1-5, and 2 points on question 6. Your score would be (30 x 1.25) + (13 x 1.875) + (2 x 3.125) = 68.125 which rounds to 68 points. By looking at the chart below, you can see that'd get you a 4 on the AP Statistics exam. Below is a conversion chart so you can see how raw score ranges translate into final AP scores. I've also included the percentage of students who earned each score in 2017 to give you an idea of what the score distribution looks like: Composite Score AP Score Percentage of Students Earning Each Score (2017) 70-100 5 13.6% 57-69 4 15.9% 44-56 3 24.8% 33-43 2 20.2% 0-32 1 25.5% Source: The College Board Where Can You Find Practice AP Stats Tests? Practice tests are an important part of your AP Stats prep. There are official and unofficial AP Stats practice tests available. Below are some of the best practice tests to use. Official Practice Tests 2012 Complete Practice Test 1997 Complete Practice Test Free-Response Questions 1998-2017 Unofficial Practice Tests Barron's Practice Test To learn more about where to find AP Statistics practice tests and how to use them, check out our complete guide to AP Statistics practice exams. 3 Tips for the AP Statistics Exam In this section we go over three of the most useful tips you can use when preparing for and taking the AP Statistics test. Follow these and you're more likely to get a great score on the exam. #1: For Free Response, Answer the Entire Question As we mentioned earlier, free-response questions on AP Stats are graded holistically, which means you'll get one score for the entire question. This is different from many other AP exams where each correct component you include in a free-response question gets you a certain number of points, and those points are then added up to get your total score for that question. The Stats free-response questions are graded holistically because there are often multiple correct answers in statistics depending on how you solve the problem and explain your answer. This means you can't just answer part of the question and expect to get a good score, even if you've answered that part perfectly. If you've ignored a large part of the problem, your score will be low no matter what. So instead of trying to get a point here and there by including a correct formula or solving one part of a question, make sure you're looking at the entire problem and answering it as completely as possible. Also, if you need to include an explanation, be sure it explains your thought process and the steps you took. If your explanation shows you understand important stats concepts, it could help you get a higher score even if your final answer isn't perfect. Aiming for the most complete response possible is also important if you can't answer one part of a question that's needed to answer other parts. For example, if you can't figure out what the answer to part A is, but you need to use that answer for parts B and C, just make up an answer (try to keep it logical), and use that answer to solve the other parts, or explain in detail how you'd solve the problem if you knew what the answer to part A was. If you can show you know how to solve the latter problems correctly, you'll likely get some credit for showing you understand the stats concepts being tested. #2: Know How to Use Your Calculator You'll need a graphing calculator to answer pretty much every question on the Stats exam, so make sure you know how to use it. Ideally, the calculator you use on test day will be the same one you've been doing homework and taking tests with throughout the school year so you know exactly how to use it. Knowing how to solve common stats functions on your calculator and interpret the answers you get will save you a lot of time on the exam. Your calculator will likely be most useful on the multiple-choice section where you don't need to worry about showing work. Just plug in the data you're given into your calculator, and run the right equations. Then you'll have your answer! #3: Know Your Vocabulary You may think that since AP Stats is a math course, vocab won't be an important part of the test, but you need to know quite a few terms to do well on this exam. Confusing right- and left-skewed or random sampling and random allocation, for example, could lead to you losing tons of points on the test. During the school year, stay on top of any new terms you learn in class. Making flashcards of the terms and quizzing yourself regularly is a great way to stay up-to-date on vocab. Many AP Stats prep books also include a glossary of important terms you can use while studying. Before the AP Stats exam, you should know all important terms like the back of your hand. Having a general idea isn't good enough. A big part of stats is being able to support your answers, and to do this you'll often need to use stats vocab in your explanations. Just stating the term won't earn you nearly as many points as being able to explain what the term is and how it supports your answer, so make sure you really know your vocab well. Summary: Statistics AP Exam The AP Statistics exam is three hours long and consists of 40 multiple-choice questions and six free-response questions. The content of the exam covers four main areas: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. To prepare well for AP Stats exam questions, it's important to take practice exams and know how to grade them so you can estimate how well you'd do on the actual test. When studying for the AP exam, remember to answer the entire question for free response, know how to use your calculator, and be on top of stats vocabulary. What's Next? Feel the need to do some quick reviewing after looking through what'll be covered on the AP Stats exam? Take a spin through our guide to statistical significance to refresh yourself on how to run a t-test. How difficult is AP Stats compared to other AP classes? Get the answer by reading our guide to the hardest AP exams and classes. Wondering which other math classes you should take besides statistics? Math is often the trickiest subject to choose classes for, but our guide will help you figure out exactly which math classes to take for each year of high school. A prep book can be one of your best study resources for the AP Stats exam. But which prep book should you choose? Check out our guide to AP Stats prep books to learn which is the best and which you should avoid. 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