Graduate Record Examinations (GRE)

Preparing to take the GRE?


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Quick Facts

Get the “need to know” information at a quick glance.


The Graduate Record Examinations (GRE) is a standardized test developed for people who are interested in attending graduate school. The GRE tests a variety of skills, such as verbal reasoning, quantitative reasoning, critical thinking, and writing, that individuals will need to succeed in graduate school, regardless of their specific field or program.


Information and table obtained from

The GRE has three content areas: Analytical Writing, Verbal Reasoning, and Quantitative Reasoning. The Analytical Writing area contains 2 writing tasks. The Verbal Reasoning area contains 2 sections, which each have 20 questions. The Quantitative Reasoning area contains 2 sections, which each have 20 questions.

You will have 30 minutes to complete each Analytical Writing task, 30 minutes to complete each Verbal Reasoning section, and 30 minutes to complete each Quantitative Reasoning section.

This means that you will have a total of 3 hours to answer the 82 questions on the exam.

Please note:

  • Unscored¹ Your version of the test may contain an unscored writing task.
  • Research² Your version of the test may contain a few unscored questions which are used for research purposes by the test-maker.


The current cost to take the GRE is $205. You will be given four free score reports and can purchase additional score reports online through your ETS account for $27 each.


So, how do you register for the GRE?

In order to register for the GRE, you must have an ETS account, which you can both create and log into by clicking here:

After creating an account and logging in, click on the blue “Register/Find Test Centers, Dates” button under the “My Tests” tab on the left-hand side of the screen. Choose “GRE General Test” from the “select a test” drop-down menu, type in your preferred location, and select the two-month period in which you’d like to take the GRE. Select a test on the following page by clicking the blue “Register” button beside an available location and date.


So, how is the GRE scored? Here’s a GRE score breakdown for you.

The Verbal Reasoning and Quantitative Reasoning sections of the GRE are scored in one-point increments on a scale of 130-170. 

The GRE is “section-level adaptive” and each of these areas is broken into two sections or “measures.” Your performance on the first measure will determine the level of difficulty on your second measure. The increased difficulty of certain questions is weighted into the final score, so while on test-taker might correctly answer 11/20 questions on the first measure and 19/20 on the second measure for a total of 30/40, their score will not be as high as someone who answered 18/20 on the first measure and 12/20 on the second measure. Within the first and second measures, each question is weighted equally.

Wrong answers do not deduct points from your overall score on the GRE, so do not leave questions blank. Instead, try to correctly answer as many questions as possible.

The Analytical Writing section is initially graded on a scale of 0-6 with half-point increments by a human reader. 

Next, an e-rater scoring engine, a computer program developed by ETS, scores the work. If the human and computer scores closely agree, then the final score is created by averaging them. If they disagree, another human reviews the essays and the final score is the average between both human-given scores.

Pass rate

A “good” GRE score depends on the program and school to which you are applying. Scores of 163-170 on the Verbal Reasoning Section, 165-170 on the Quantitative Reasoning Section, and 5.0-6.0 on the Analytical Writing Section will put you in the top 10% of test-takers. Verbal Reasoning scores of 158-162, Quantitative Reasoning scores of 159-164, and Analytical Writing scores of 4.5 are considered competitive and will place you in the top 25% of all test-takers.

To fall around the 50th percentile of all test-takers, you’ll need to score 151-152 on the Verbal and Quantitative Reasoning Sections and 4-3.5 on the Analytical Writing section.

Rember, the most important reason for achieving a “good” score is that a high score will get you into a graduate program you’re excited about. Understanding the requirements or minimums at the schools you’re applying to will help you create a target score.

Study Time

While everyone has different study practices and initial knowledge bases, it is generally recommended that test-takers spend at least two to three months studying for the GRE. The amount of time you need to spend preparing for the GRE depends upon the score you’d like to achieve and your existing familiarity with the material on the test.

You should also take a complete, timed practice test at least once before the actual exam. This will give you a better idea of how to pace yourself, where your weaknesses are, and how much time you’ll need to spend preparing for the GRE. As a very rough guideline, test-takers can generally improve their overall score in one section by five points after forty hours of studying. Taking a practice test early and repeating the process throughout the months before the real exam will allow you to create goals and track your progress.

What test takers wish they would’ve known:

  • It’s important to do your best when answering every question. The GRE is a computer adaptive test. That means that each question you answer correctly or incorrectly will determine subsequent questions you receive. 
  • Place equal importance on verbal questions and other questions. Many test-takers do not realize that being able to communicate properly is crucial to success in both the business world and in other fields. Remember, the more you can improve your responses to the verbal questions, the more you can improve your overall score.
  • If you are unsure of the answer to a question, you should try to eliminate as many answer choices as possible before selecting one. This increases your odds of answering the question correctly. There are no penalties for wrong answers on the GRE.
  • It is best to relax and focus on the main ideas of the passages which you are presented with. Remember, you do not need to memorize the details of the content. Some test-takers find it helpful to take a couple of notes as they read to stay focused.
  • After reading a question, do not immediately select an answer choice. Instead, “pre-think” the answer before reading the answer choices. This will actually work to save you time.
  • If you find yourself staring at a question for 30 seconds and it is still not making sense to you, just choose the best answer and move on. While you want to consider questions carefully, if an answer is not coming to you, it is better to keep moving than to waste time.
  • When you are preparing for the GRE, take multiple practice tests. This will not only help you figure out what you need to study, but it’ll acclimate you to the ways questions are worded and the feeling of taking a timed test. The more practice tests you’ve taken, the more relaxed you’ll be on test day because you’ll know what to expect.

Information and screenshots obtained from the web site.

Analytical Writing

The Analytical Writing measure tests your ability to think critically, write analytically, and articulate complex ideas with clear arguments and focused direction. You will encounter two prompts, Analyze an Issue and Analyze an Argument. You will be given 30 minutes to respond to each of the two prompts.

This content area can be neatly divided into three sub-content areas:

  • Analyze an Issue
  • Analyze an Argument
  • Writing Style and Mechanics

So, let’s talk about them.

Analyze an Issue

The Analyze an Issue task asks test-takers to think critically and clearly express their opinion about a contemporary topic. Each prompt will introduce an issue that can be viewed and argued from a variety of perspectives; you will be asked to agree or disagree. Successful responses choose a clear side, articulate a logical argument, and provide compelling evidence.

Let’s look at an example of an Analyze an Issue prompt:

Because of the role technology plays in contemporary society, educational institutions should make computer literacy classes mandatory for all high school students to better prepare them for the changing job market.

Discuss the extent to which you agree or disagree with the statement and explain your reasoning for the position you take. In developing and supporting your position, you should consider ways in which the statement might or might not hold true and explain how these considerations shape your position.

Analyze an Argument

The Analyze an Argument task will test your ability to analyze a given argument, evaluate its logical soundness, and compose a clear critique. You will be presented with a short passage that contains an argument and instructions about how to respond. 

Scorers will analyze how well you follow the given instructions, analyze relevant aspects of the argument, and clearly express yourself with effective reasons and examples. You will not be asked to provide your own opinion on the topic.

Let’s look at an example of an Analyze an Issue passage:

Nature’s Way, a chain of stores selling health food and other health-related products, is opening its next franchise in the town of Plainsville. The store should prove to be very successful: Nature’s Way franchises tend to be most profitable in areas where residents lead healthy lives, and clearly Plainsville is such an area. Plainsville merchants report that sales of running shoes and exercise clothing are at all-time highs. The local health club has more members than ever, and the weight training and aerobics classes are always full. Finally, Plainsville’s schoolchildren represent a new generation of potential customers: these schoolchildren are required to participate in a fitness-for-life program, which emphasizes the benefits of regular exercise at an early age.

Write a response in which you examine the stated and/or unstated assumptions of the argument. Be sure to explain how the argument depends on these assumptions and what the implications are for the argument if the assumptions prove unwarranted.

Passage obtained from the ETS website: 

Other Analyze an Argument prompts might ask you to: 

  • Discuss what questions need to be answered in order to determine if an argument is reasonable
  • Explain what evidence that is needed to evaluate a given argument and how that evidence would either strengthen or weaken it
  • Introduce alternative explanations that could rival an explanation that the prompt provides

Understanding the Prompt and Brainstorming

Be sure to read and re-read the prompt to make sure that you correctly identify your task, then write down your initial reactions and thoughts. Brainstorm the implications of the argument or issue, any assumptions made, and questions you have about it. 

Structuring Your Essay

Make sure to include a clear thesis statement at the end of your introduction that introduces the main ideas you will discuss in your essay. Focus on making sure that your thesis answers the prompt’s instructions directly and clearly.

Everything you include in your essay should support your thesis statement.

Organize your ideas logically and connect them with smooth transitions. While many writers have different approaches to organizing and outlining essays, many find it helpful to follow a M.E.A.L. plan. For every body paragraph, sketch your Main Idea, Evidence, Analysis, and Link, or transition to the next topic. 

Finish your essay with a concluding paragraph. This helps the grader know that you did not run out of time and it gives you an opportunity to summarize your main arguments. Your conclusion should not introduce any new topics. In your conclusion, restate your thesis in different words.

Writing Style and Mechanics

Readers will not only grade the effectiveness of your arguments and how they are organized but also your command of standard English conventions. 

While minor grammatical errors will not be catastrophic, tonal problems, repetitive syntax, or obvious mechanical mistakes can have a negative effect on your final score.


Your responses should have a formal, academic tone. This does not mean that you cannot add flair with detailed language and colorful word choices, but it does mean that you want to avoid being overly casual or too conversational.


To create essays that are interesting to read and don’t feel repetitive, be purposeful with your syntax by varying your sentence structure to match your arguments. Long sentences often convey a feeling of overwhelming evidence, while short sentences can punctuate important points. 


Although readers understand that it can be nearly impossible to produce a completely error-free essay under strict time constraints, essays should have as few mechanical errors as possible. Using a variety of punctuation marks, such as colons and semicolons, will illustrate your strong command of English grammar and can help you create essays that are mechanically interesting. Don’t employ punctuation marks if you aren’t sure how to use them: stick to what you know, focus on writing clearly and succinctly, and when in doubt, leave it out.


Subject-Verb Agreement 

When you’re writing, one of the most important things is to maintain subject-verb agreement at all times. The subject of a sentence, or the thing doing something, must agree with the verb, or the thing being done. If a subject is singular, then the verb must also be singular.

When the subject of a sentence contains two or more nouns connected with the word “and,” use a plural verb. For example: 

  • “Betty and Jimmy are in my class.” (Correct)
  • “Betty and Jimmy is in my class.” (Incorrect) 

Collective nouns are words that imply a multitude of things or people but are treated as singular words. They can make it difficult to use the correct verb tense. Collective nouns describe groups, which, in sentences, are treated as singular units. 

For example, “The committee decides these things” is correct. While “committee” refers to a group of people, the word is singular. Therefore, the verb is also singular.

Pronoun-Antecedent Agreement

A pronoun is a word that is used in place of a specific noun. 

Words like “he,” “she,” “her,” “theirs,” “they,” and “whom” are all examples of pronouns. 

Pronouns are commonly used when repeating someone’s name would be repetitive or when a replacement word is necessary. 

For example, “Betty lost Betty’s shoes yesterday,” sounds redundant, so “Betty lost her shoes yesterday” sounds more appropriate.

The antecedent is the noun that the pronoun is referring back to: in this case, it’s “Betty.” Pronouns must always agree with their antecedents in number. 

For example, “Betty lost their shoes yesterday” is incorrect.

Singular indefinite pronouns include the words such as “each,” “either,” “one,” “anyone,” or “everything.”). 

For example, in the sentence “Everyone has to check his or her backpack for mud before bringing it inside,” the word “everyone” is singular, so “his or her” must be used to express singular possession. “Everyone has to check their backpack for mud before bringing it inside” would be incorrect.

Plural indefinite pronouns (words like “both” and “many” which refer to multiple individual things without a collective noun) require plural pronouns. 

For example, “Several of Nancy’s dogs buried their bones.”

Verbal Reasoning

The Verbal Reasoning measure has 40 questions, split into two equal sections with 20 questions each. You will have thirty minutes to complete each section.

This content area can be neatly divided into three areas:

  • Reading Comprehension
  • Text Completion
  • Sentence Equivalence

So, let’s talk about them.

Reading Comprehension

Reading Comprehension items will require you to read a passage and answer 1-6 questions about it. These questions can be divided into 6 categories:

  1. Main Idea
  2. Summarization
  3. Inference
  4. Supporting Details
  5. Author’s Perspective
  6. Vocabulary

The Reading Comprehension section will require you to actively engage with passages, identify strengths and weaknesses of given positions, consider different perspectives, draw conclusions, and distinguish between main ideas and supporting details. The passages in this section will be about physical or biological science, social science, business, contemporary issues, or the humanities.

Some questions will ask you to select a single answer and some will require you to select multiple correct answers.

Let’s take a look at the 6 question types.

Main Idea

It’s important to distinguish between main ideas and minor points. Try, in your own words, to state what the primary point of the passage is before answering questions. These questions might ask about the main idea of a paragraph or the passage as a whole.

Main Idea questions can take several forms, including:

  • The primary purpose of this passage is to…
  • Select the sentence from the passage that does NOT support the main idea.
  • Which of the following sentences would serve as the most logical addition to the paragraph’s main idea?


Summarization questions will ask you to select an answer that effectively paraphrases or restates information or an opinion found in the passage. To answer these questions, briefly consider what you think the correct answer is before reading the given choices, then find which answer best matches your opinion. 

Here are some examples of Summarization questions:

  • According to the passage, what is it about the 2006 flood that caused such a great impact on public opinion?
  • From the passage, how did church hymns influence Emily Dickinson’s poetry?
  • According to the passage, why was the Harvard study about open office plans so influential? 


Inference questions will ask you to take the information provided in the text and extrapolate a logical perspective or conclusion from it. You will need to understand what a passage implies rather than what it clearly states.

Inference questions can come in a variety of formats, including:

  • This passage most likely appeared as part of…
  • Given the author’s position on the labeling of GMO foods, what stand would the author most likely take on the issue of bioengineered meat?
  • This passage implies which of the following about…

Supporting Details

Supporting detail questions will ask you to find textual evidence within the text that supports a claim, an idea, or an opinion.

Here are some examples of how these questions may appear on the exam:

  • Which of the following ideas are supported in the passage?
  • Select the sentence that is NOT a major detail that supports the author’s opinion.
  • Select the sentence that best explains the recent discovery about lunar maria.
  • Which of the following is the most significant detail about the study reported in The American Journal of Medicine?

Author’s Perspective

Author’s Perspective questions will ask you to describe the author’s tone, perspective, or stance. Although these questions require a level of inference, the passage will always contain evidence for the correct answer. Consider the examples and evidence the author uses and the connotations of the words he or she chooses.

These questions may take a variety of forms, including:

  • Based on the passage, the author evidently believes that…
  • Based on the passage, it is likely that the author would agree with which of the following statements?
  • Which of the following expresses the author’s opinion about harmful algal blooms?
  • Select the sentence that most accurately states the author’s opinion.


Vocabulary questions will always ask about vocabulary in context. While more than one option might fit the word’s general definition, only one answer will match the word’s meaning in the given context. Plug the different answer choices into the passage and choose the one that most logically completes the sentence.

Vocabulary questions often look something like this:

  • In this passage, “dynamic” (line 43) means…

Text Completion

Text Completion questions include a short passage with one, two, or three blanks. 

You will be asked to select words to fill in each of these blanks. You will be given 6 answer choices for single blank questions and three answer choices for each blank for double and triple blank questions.

These questions will test your vocabulary and ability to interpret information from a given sentence. The missing word or words will be crucial and you will need to use context clues to find the correct answer(s). 

Partially correct answers do not receive any credit. It is important that each blank is correctly filled.

“Cue” Words

Text Completion passage will often include words like “although,” “however,” or “moreover.” If you don’t read the passage carefully, you might miss an important word that changes the appropriate answer.

Let’s try an example question:

Although many people believe that acupuncture, a practice which is said to allow a practitioner to affect the body’s “energy flow,” is __________, others believe that this therapy is perfectly __________.

In this question, “[a]lthough” is an important cue word because it tells you that the first blank needs to contrast with the second blank. 

The correct answers are:

Blank (i) A. fallacious
Blank (ii) B. rational

Inferring Meaning Through Context

To infer meaning from context, read carefully to make sure you understand the message. Pay attention to any connotations already present in the passage, and try to think of a word of your own that would fill in the blanks without substantially changing the passage’s meaning. See if any of the answer choices match or are similar to your word. 

You do not need to fill in the first blank first: sometimes starting with the second or third blank will be easier. When you are done, read the entire sentence with your chosen answers to make sure it is logical and grammatically correct.

Sentence Equivalence

Sentence Equivalence questions have one blank: you must choose two words from the answer bank that could both complete the sentence and give it roughly the same meaning. There is no credit for partially correct answers. BOTH of your choices must be correct.

Let’s look at an example:

Although many considered it to be a(n) ______ time at the company, Jenny’s day-to-day work was almost exactly the same as it was before the new CEO took over.

  1. monotonous
  2. dynamic
  3. volatile
  4. innovative
  5. ordinary
  6. suitable

To answer these questions, first, plug each answer choice into the sentence and eliminate any words that do not make sense. 

Choices A and E, “monotonous” and “ordinary,” do not make sense because the word “[a]lthough” conveys that the company is somehow shifting despite the way Jenny’s work hasn’t changed. Choice C, “volatile,” has a negative connotation and the other choices do not, so it cannot be correct. 

Choices B and choice D are similar in meaning, but F is not similar to either of these. Therefore, B and D are correct.

Quantitative Reasoning

The Quantitative Reasoning Measure is divided into two sections. There are 20 questions on each section. You will have 35 minutes to complete each 20-question section.

The questions on the test may be multiple-choice, numeric entry, or comparison questions. For each comparison question, you will be given two values and you must determine whether one value is greater, if the values are the same, or if there is not enough information to answer the question.

This Quantitative Reasoning Measure can be neatly divided into 4 sub-content areas:

  • Arithmetic 
  • Algebra
  • Geometry
  • Data analysis 

So, let’s talk about them.


First, let’s discuss some concepts which you are likely to find in basic arithmetic questions, such as number properties, order of operations, exponents, and number sequences. We will also review the relationships between time, rate, and distance. You will need to understand these concepts to perform well on the exam.


We briefly mentioned exponents when reviewing the order of operations. Let’s take a closer look at them now.

Here are a few rules to know when working with exponents:

Number Sequences

Number sequences often appear on the GRE. For example, you may be asked to determine the nth term in a sequence. 

Here is an example of how this concept may appear on the exam:

Find the next 2 numbers in the sequence. Mark ALL answers that are correct.


  1. 9
  2. 13
  3. 21
  4. 24
  5. 26
  6. 34

The correct answers are B and C. In this case, the next term is always found by adding the two numbers which precede it. 5 + 8 = 13 and 8 + 13 = 21.

The key is to ask yourself how each number relates to the other numbers. Here is another example problem:

What is the 6th term in the sequence 13, 19, 35, 67,…?

  1. 56
  2. 63
  3. 127
  4. 131
  5. 256

There are 4 given terms. That means that we must find term 5 as well as term 6. Here, each number is found using 2n+2 + 3.

Term 1: 2n+2 = 21+2 = 23 = 8 (Now add 3.) = 13
Term 2: 2n+2 = 22+2 = 24 = 16 (Now add 3.) = 19
Term 3: 2n+2 = 23+2 = 25 = 32 (Now add 3.) = 35
Term 4: 2n+2 = 24+2 = 26 = 64 (Now add 3.) = 67
Term 5: 2n+2 = 25+2 = 27 = 16 (Now add 3.) = 131
Term 6: 2n-1 = 26+2 = 28 = 32 (Now add 3.) = 256

Now that we’ve reviewed number sequences, let’s explore time, rate, and distance.

Time, Rate, and Distance

We discuss time, rate, and distance all of the time–often without even realizing it. For example, you might say that you drove 55 miles per hour. That would be the rate at which you traveled. 

Let’s review how these variables relate. In the following formulas, t = time, d = distance, and r = rate.

So, if Kevin rides his bike for 2 hours and travels for 24 miles, his rate of speed is 12 mph. Why? Because the distance (24) divided by the time (2) is equal to 12.

Now, let’s try a sample problem.

Allen runs 200 meters in 25 seconds. If he travels at the same rate, how many meters is he able to run in 90 seconds?

First, we need to find Allen’s rate.

r = d / t so Allen’s rate is r = 200 / 25 = 8 meters per second

Now, we need to plug in Allen’s rate and the time (90 seconds) to find the distance.

d = rt so the distance is d = (8)(90) = 720

Allen is able to run 720 meters in 90 seconds!


On the Quantitative Reasoning portion of the GRE, you will need to show your algebra skills by performing tasks such as simplifying expressions and working with linear equations.

Let’s review these concepts together now!

Simplifying Algebraic Expressions

On the test, it is likely that you will need to simplify expressions. In order to do this, you must combine like terms. Remember that the numbers in algebraic expressions are variables. Variables may only be combined with like variables.

A number that stands on its own is called a constant. The number before a variable is a coefficient. For example:

4x + 7 + 2y

In this example, 4 and 2 are coefficients and 7 is a constant. Both x and y are variables, and they cannot be combined using addition. Therefore, the expression is in its simplest form.

Let’s simplify an expression step by step now:

2(x² + y) + 4x + 17 + 3(y²) + 10x + 8 + √25

First, let’s solve the parentheses:

2(x² + y) + 4x + 17 + 3(y²) + 10x + 8 + √25 =

2x² + 2y + 4x + 17 + 3y² + 10x + 8 + √25 

Now, let’s find the square root of 25 so that we have as many like terms as possible:

2x² + 2y + 4x + 17 + 3y² + 10x + 8 + √25 =

2x² + 2y + 4x + 17 + 3y² + 10x + 8 + 5

Now, we must move our like terms together: 

2x² + 2y + 4x + 17 + 3y² + 10x + 8 + 5 =

2x² + 2y + 3y² + 10x + 4x + 8 + 5 + 17 

Add the like terms:

2x² + 2y + 3y² + 14x + 30

Since there are no more like terms, we are all set! We’ve simplified the expression as much as possible.

Linear Equations

A linear equation can be used to describe a line on the coordinate plane.

The standard form of a linear equation is ax + by = c. So, 2x + 3y = 5 is an example of a linear equation in standard form.

Note that linear equations do not always appear in standard form. Here is the same equation in nonstandard form: 1x + 3y = 5 – 1x. Notice that the only difference in that example is that 1x was moved to the opposite side of the equation.

The x-intercept is where the line crosses the x-axis (y = 0) and the y-intercept is where the line crosses the y-axis (x = 0).

Let’s look at a linear equation in standard form and find the x-axis and y-axis in order to graph it. Here’s our equation:

9x + 16y = 72

Let’s find the x-intercept first by finding out what x is when y = 0. Let’s get rid of y first.

9x + 16y = 72

9x = 72

Now we can divide 72 by 9 to get x = 8.

Now let’s make x equal to zero.

9x + 16y = 72

16y = 72 

y = 4.5

Now we can graph each of the two points, (8, 0) and (0, 4.5) and draw a line to connect them:


Next, let’s look at some algebra concepts that often appear on the GRE Quantitative Reasoning measure.

Perimeter and Area

Recall that the perimeter of a figure is the measure around the outside of a figure. The area of a figure is the measure of the two-dimensional space inside of a perimeter. Note that area is measured in square units. 

Let’s review some perimeter and area formulas and look at some examples.

Keep in mind that on the exam, perimeter and area questions may appear in the form of word problems. For example, you may be asked to consider the perimeter of a rectangular pool or field.


Instead of using the word perimeter, we refer to the distance around the outside of a circle as circumference.

The diameter (d) of a circle is a straight line that passes from one side of the circle to the other. The radius (r) of a circle is half of the diameter. 

To calculate the circumference of a circle use the formula C = 2πr.

For example, imagine a circle with a radius of 16 inches. To find the circumference of the circle, we would plug that value into the formula (2π16) to find that its circumference is 100.531 inches (rounded).

In geometry, an arc is a portion of the circle’s circumference. 

Formula to find the length of an arc: 

Length = (central angle / 360)(circumference)

Take a look at the following circle. The area shaded green represents the central angle:

Let’s say that the central angle is equal to 120° and the circumference of the circle is 30 feet. Now, we’ll plug those measurements into our formula.

L = (120 / 360)(30) = (⅓)(30) = 10

So, the length of this arc is 10 inches, which is exactly a third of the circumference.

Data Analysis

Next, let’s take a look at some data analysis concepts and discuss how they might appear on the Quantitative Reasoning portion of the GRE. 

Mean, Median, and Mode

Next, we will review mean, median, and mode, which are measures of central tendency. Let’s use an example data set. The list below gives the weights of 9 dogs.

Weight (in pounds): 64, 46, 34, 70, 15, 14, 45, 75, 70

First, we will order the list from least to greatest (ordering the list from greatest to least is also effective).

Weight (in pounds): 14, 15, 34, 45, 46, 64, 70, 70, 75

Mean: Sum divided by the total. 433 pounds ÷ 9 dogs = 48.111
Median: The value in the center of the ordered list. 46
Mode: The value which occurs most often. 70


Next, we’ll review some concepts related to probability.

Probability of a Single Event

Probability refers to the likelihood that an event will occur. For example, the probability of a coin landing in the “heads” position is 0.5. In other words, there is a 50% chance of this outcome. No matter how many times the coin is flipped, the probability of this outcome stays the same.

The probability (P) of an event (E) can be expressed as:

So, the probability of drawing a specific card from a deck of 52 cards is:

(P)E = 1 / 52 = which is about .019 or 1.9%

Probability of Compound Events

Now, think about the probability of drawing a specific card and then drawing a second specific card. This scenario is a little bit different because it deals with compound events.

If a card is drawn from a deck and replaced before a second card is drawn, each time a card is drawn is an independent event. These outcomes do not affect each other.

Imagine that you have a bag of 5 marbles and each marble in the bag is a different color. You also have a package of 10 candies and each candy is a different flavor. First, you remove a marble, then you remove a candy.

Removing the marble has no effect on what type of candy you remove and vice versa.

So, what is the probability of drawing a purple marble from the bag, then drawing a strawberry-flavored candy from the package? The first event, drawing the marble, may be expressed as P(A). The second event, drawing the candy, may be expressed as P(B).

P(A and B) = P(A) ∙ P(B)

Probability of drawing a purple marble (1 / 5) and a strawberry candy (1 / 10):

P(A and B) = (1 / 5) ∙ (1 / 10) = (1 / 50) = 2%

There is a 2% chance of achieving these two outcomes.

Just as there are independent events, there are dependent events. For example, if you draw a card from a deck and do not replace it before drawing another, the first event affects the second event. 

Conditional probability may be expressed as: 

P(A and B) = P(A) ∙ P(B|A)

Let’s solve an example problem.

Freya randomly draws two cards from a deck of 52 cards without replacing the first card. What is the likelihood that both cards she draws are queens?

P(A and B) = P(A) ∙ P(B|A)

P(A) = (4 / 52)
P(B|A) = ∙ ( 3 / 51) Notice that there are now fewer cards!
P(A and B) = (4 / 52) ∙ (3 / 51) = (12 / 2562) = (1 / 221) = about .0045

We can round .0045 to determine that Freya has about a .5% chance of drawing two queens.

Tables and Graphs

Often, data appears in the form of tables and graphs the Quantitative Reasoning measure. Let’s review those concepts now.


You can see an example of a frequency table below. This table shows the quiz scores of a group of students.

Think back to measures of central tendency. If you were asked to find the median score, you would list all of the scores in order from highest to lowest (or vice versa).

70, 74, 77, 80, 83, 83, 86, 86, 86, 90, 90, 90, 90, 92, 94, 94, 98

Based on the table, you can determine that 86 is the median score. Remember to refer to both sides of a frequency table. For this example, it is important to know how many students made each of the grades listed.


Below, you can find an example of a bar graph as well as an example of a histogram.

Notice that the information in both the histogram and the bar graph is the same. The difference is that the bars on a histogram touch.

Let’s look at a second bar graph now and answer an example question.

The following bar graph shows the number of novels a public library purchased over the course of three months.

There were _____ more novels purchased in February than in April.

For this question, we can ignore the middle bar, which represents March. In February, the library purchased 40 novels and in April, the library purchased 35 novels. So that’s a difference of 5 novels.

And that’s some basic info about the Quantitative Reasoning measure.