# Praxis Core For Dummies with Online Practice Tests

**Published: **02-26-2020

**Score high on the Praxis Core and jumpstart the teaching career of your dreams!**

*Praxis Core For Dummies *is a must-have resource for preparing for—and passing—the Praxis® Core Academic Skills for Educators Exam. The best way to succeed on any exam is to prepare with plenty of practice questions. This book provides you with 2 full-length practice tests **plus** an additional 4 tests online. That’s **6 complete tests** containing the same kinds of questions you will see on the reading, writing, and mathematic sections of the exam!

Now in its third edition, *Praxis Core For Dummies* has been carefully updated to align with changes in the Praxis Core exam, including new mathematics subtests and revised overview information**. **A thorough summary of the exam shows you exactly what to expect on exam day, while in-depth content reviews help you fully understand each section of the test.

- Find out what you need to know for every section of the exam
- Test yourself with full-length practice tests in the book and online
- Get the most up-to-date info on the latest test changes
- Use effective study strategies for keeping a cool head and a sharp mind
- Set yourself up for success

Practice your way to test-taking perfection with the help of *Praxis Core For Dummies.*

## Articles From Praxis Core For Dummies with Online Practice Tests

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Cheat Sheet / Updated 03-09-2021

Before you get too excited, understand that the information that follows isn’t actually about how to cheat on the Praxis. It’s really more about the most efficient ways to prepare for the exam. But “preparation sheet” doesn’t quite have the same ring to it. Besides, cheating is unnecessary if you know what you’re doing, and sometimes figuring out what to do is actually easier. As Bart Simpson once said after accidentally studying for a test, “It was like a whole new way to cheat!”

View Cheat SheetArticle / Updated 02-24-2020

When you first began looking into what is or isn’t tested on the Praxis writing exam, your reaction to finding out that there were questions about capitalization was probably something like “There are questions about capitalization on this test?! What am I, in third grade?” Yes, you almost certainly already know that the first letters of the first words of sentences are capitalized, as are people’s names; the names of proper places like cities, states, or countries; the names of companies like “Facebook”; the names of sports teams and bands; and the words in the titles of books, movies, and so on. You may not, however, know some of the trickier rules about capitalization, and those are the ones that the Praxis writing test will ask about. Here’s a rundown of the most common capitalization-related tricks: Titles, like “president”: Titles, such as “president,” “mayor,” and so forth, are only capitalized when they are placed before the name of, or used to indicate, a specific president or mayor or what have you. So, you should write “Abraham Lincoln was the 16th president,” but “Everyone knows that President Lincoln wore a stovepipe hat.” If you’re talking about the current president (or mayor, or whomever), you capitalize the word even if the person’s name doesn’t appear in the sentence, because you’re still indicating a specific person: “The President held a press conference this morning.” The same rule applies for God versus a god: You capitalize “God” when referring to a/the deity with the proper name God, but not when you’re talking about deities in general: “I prayed to God that I would pass the test” versus “Apollo was one of the Greek gods.” The names of seasons: Many people are unclear about this, but the rule is that the names of seasons are only capitalized if you are addressing the season directly, as you might in a poem. So, you say “I love the way the leaves change color in the fall,” but “Oh, my beloved Fall, how I love it when your leaves change color!” The names of specific regions, even if they are not actual countries: You should capitalize the names of all proper nouns, and that includes geographical areas that are not technically specific countries, cities, and the like: “My uncle frequently travels to the Far East.” You should not, however, capitalize the names of cardinal directions when they’re just used to indicate directions rather than an areas: “My uncle has to fly east to get to the Far East.” You should also not capitalize the “cardinal direction” part of a name when a suffix is attached to it, because that involves a comparison rather than a proper name, with the exception of cases where the cardinal direction with a comparative suffix is part of an actual proper noun: “Many people don’t realize that northern Brazil lies in the Northern Hemisphere.” Specific eras in history: The title of a specific period in history, even a slang or unofficial one, is a proper noun and should be capitalized accordingly: “The Disco Era was mercifully short-lived.”

View ArticleArticle / Updated 02-24-2020

Correctly answering selected-response items on the writing portion of the Praxis requires that you read each question carefully. Where possible, put the question into your own words. Be sure to read every choice before you make your selection. Eliminate the obviously wrong choices The process of elimination can help you choose the correct answer in a selected-response question. Start by crossing off the answers that couldn’t be right. Then spend your time focusing on the possible correct choices before selecting your answer. Doing so greatly increases the odds of your choosing correctly. Pay special attention to answers that contain these words: none, never, all, more, always, and only. These words indicate that the answer is an undisputed fact and, consequently, isn’t likely to be the correct choice. Conditional words like usually or probably make the answer more likely. Be particularly careful of selected-response questions using the words not, least, and except. These questions usually ask you to select the choice that doesn’t fit. Stay alert! It’s easy to misread these questions. Don’t be afraid to say it’s right the way it is Although it may seem counterintuitive, if a sentence is correct as written, “No error” is the correct answer. Fear not: some tasks will be written correctly. Just be sure to consider all the choices before making your decision. The art of guessing as a last resort Your score is based on the number of correct answers. You’re not penalized for incorrect answers. For this reason, you should answer every question. If you face a difficult question, narrow your choices as much as possible and, if necessary, guess! Don’t spend too much time considering a difficult question. Mark the question and come back to it. Answer the easy questions first. You’re not expected to answer all the questions correctly. In order to pass the Praxis, you must simply achieve the minimum passing score for your state. A word of advice about “trusting your ear” If you grew up in a family of English teachers who corrected your every incorrect utterance, complete with an accompanying grammar lesson, it’s probably pretty safe for you to “trust your ear”; that is, whatever sounds right to you is likely to be right. However, if you’re like most people, you grew up in a family that was considerably less interested in your grammar. Language that sounds right to you is simply language you’re accustomed to hearing and may very well be incorrect. Play it safe and analyze the sentence carefully. It’s easy to make a mistake when “trusting the ear.” Consider some examples. Neither the boys nor the girl (is/are) paying attention. While “are” may sound right, the correct answer is “is.” The verb agrees with the closest subject when subjects are compound. I will split the cost between you and (I/me). You probably hear someone use the incorrect construction of “between you and I” pretty often. Just because you hear it spoken, though, doesn’t mean it’s correct grammar. Objects of the preposition must be objective case, so “me” is the pronoun to use here. You and (I/me) should see that new movie. In this example, the personal pronoun is being used as one of the subjects of the sentence. Subjects must be nominative case, so “I” is the correct choice here.

View ArticleArticle / Updated 02-24-2020

For the Praxis Core exam, you need to become familiar with many ways to display or represent your data. Using lists, tables, graphs, charts, and plots to represent data is a surefire way to make sure you aren’t tricked by the data. These methods of organizing data can also help you see patterns more readily. In the sections that follow, you become skilled at dissecting and interpreting different types of data representations. Tables When you have gobs of data about a particular subject, you can sort, analyze, and display your data in a table. Tables only work if you have at least two sets of data to be organized into columns and rows. When working with tables, make sure to pay attention to the title of the table; it helps you understand what data to analyze. Next, notice the column and row titles. In the following table, the data for the types of flowers and the number of each type of plant in Mary’s flower bed are listed. Make sure to read your question carefully and dissect the data accordingly. Which ratio compares the number of rose plants to the number of daffodil plants? A. 3:2 B. 2:3 C. 4:3 D. 5:6 E. 3:4 The correct answer is Choice (B). The ratio of roses to daffodils is 8:12; when factored, the ratio is 2:3. The Praxis Core exam will expect answers in the simplest form. Bar graphs and line graphs A bar graph uses the length of vertical or horizontal bars to represent numbers and compare data. Bar graphs are good to use when your data is in categories. Bar graphs must contain a title, axis labels for the horizontal and vertical axis, scales, and bars that represent numbers. The following bar graph shows the number of canned goods collected by homerooms at Cardozo Middle School. Mr. Smith’s homeroom collected more cans than how many other homerooms? A. 3 B. 4 C. 5 D. 6 E. 7 The correct answer is Choice (A). Use the graph to compare the number of cans collected by each homeroom. According to the lengths of the vertical bars, Mr. Smith’s homeroom collected more cans than Mr. Lewis, Mr. Davis, and Mrs. Reed’s classes. Line graphs are graphs that show data that is connected in some way over a period of time. Suppose you’re preparing for a statistics test and each day you take a short online quiz to see how you’re progressing. These are the results: Day 1 30 percent Day 2 20 percent Day 3 50 percent Day 4 60 percent Day 5 80 percent After you’ve created a table from your results, display them in a line graph. You can then decide, based on your progress on the practice quizzes, how likely you are to pass your statistics test. What trends do you see in the following graph? The graph indicates that as the days of practicing the online quizzes increase, your score increases; so, you will, more than likely, pass your statistics test. Pie charts Are you ready for a slice of pie? Pie charts are also known as circle graphs. These graphs focus on a whole set of data that is divided into parts. Each category represented in a pie chart is represented by a part, called a sector, of the interior of the circle. The portion of the circle interior a category’s sector takes up is part of what represents the portion of the whole (population, number of items sold, and so on) the category makes up. For example, if a pie chart represents categories of county government spending and 10 percent of the county government spending goes to road maintenance, the category of road maintenance would be labeled in a sector that takes up 10 percent of the interior of the circle. The sector would also have “10%” presented in it, and the sector would be labeled with “Road Maintenance.” Move the decimal point two places to the right and add a percent symbol. Multiply the percent by 360 to get the number of degrees for that slice of your pie chart. Display all the slices together in the pie chart. The following table shows the conversion of raw data to information that can be used to create a pie chart. The resulting pie chart is shown in the example question. When reading a pie chart, the larger the value, the larger the piece of pie! Stem-and-leaf plots A stem-and-leaf plot blossoms into a useful graph when analyzed properly. You usually use this type of graph when you have large amounts of data to analyze. You can analyze data sets such as classroom test results or scores of the basketball team using a stem-and-leaf plot. Based on place value, each value in your data set is divided into a stem and leaf. What each stem and leaf plot represents is indicated by a Key. Draw a vertical line to separate the stem from the leaf. The leaf is always the last digit in the number. The stem represents all other digits to the left of the leaf. To divide 105 into stem-and-leaf format, you draw a line to separate the stem from the leaf, which indicates a stem of 10 and a leaf of 5. Say you have the following numbers: 50, 65, 65, 60, 50, 50, 55, 70, 55 The first step is to arrange your data in least-to-greatest order, as follows: 50, 50, 50, 55, 55, 60, 65, 65, 70 Now arrange these numbers vertically in a table: Math Test Results Stem Leaf 5 0 0 0 5 5 6 0 5 5 7 0 Key: 5|0 means 50 This arrangement allows you to quickly identify your stems. Your stems in the data set are 5, 6, and 7. You have five data values in the list in the 50s: 50, 50, 50, 55, and 55. The leaves that go along with the 5 stem are 0, 0, 0, 5, and 5. You have three data values in the 60s: 60, 65, and 65. The leaves that go with the 6 stem are 0, 5, and 5. Finally, you have one leaf with a data value of 0 to accompany the stem of 7. When using a stem-and-leaf plot, you can quickly identify the least and greatest values in the data set (50 and 70), calculate the range (), and calculate the median or middle number (55). The following data shows the number of people visiting a particular frozen yogurt shop per hour across a 12-hour day. Hourly customers: 4, 17, 22, 31, 39, 40, 25, 43, 35, 40, 38, 13. When this data is arranged in a stem-and-leaf plot, you get the following diagram. Use it to answer the questions that follow. Hourly Customers Stem Leaf 0 4 1 3 7 2 2 5 3 1 5 8 9 4 0 0 3 Key: 4|0 means 40 What was the largest number of people that entered the shop during an hour? The correct answer is 43. Based on the diagram, the highest stem is 4 and the highest leaf in that stem is 3. Box-and-whisker plots Box-and-whisker plots, also known as box plots, show different parts of a data set using a line of numbers that are in order from least to greatest. A box-and-whisker plot allows you to divide your data into four parts using quartiles. The median, or middle quartile, divides the data into a lower half and an upper half (for more on finding the median, see the later section “Measuring arithmetic mean, median, or mode”). The median of the lower half is the lower quartile. The median of the upper half is the upper quartile. Your data set will contain the following five parts: The least value: The smallest value in the data set. The lower quartile: The median of the lower half of the data set. The median: The median or middle quartile. This divides the data into a lower half and an upper half. The median is the number in the center. If two numbers are in the center, find the average of the two middle values. The upper quartile: The median of the upper half of the data set. The greatest value: The largest value in the data set. The following diagram shows how data is dissected using a box-and-whisker plot. To create a box-and-whisker plot, follow the diagram below. The diagram begins with the data set. The data set is then put in least-to-greatest order. Underline the least value and the greatest value in the data set. Then find the median of the entire data set. Remember, when calculating the median, if there are two values in the center of a data set, find their average. The median divides the data set into the lower set and higher set. You must then find the median of the lower set. That is the lower quartile, or Q1. You also must find the median of the upper set. That median is the upper quartile, or Q3. The median of the entire set of data is Q2. The word “quartile” can also be used to refer to a division of numbers marked off by Q1, Q2, Q3, or the highest number in the entire set. After dissecting the data into the five values, graph the five values on a number line. Draw a box from Q1 to Q3. Draw a vertical line inside the box at Q2. The lines connecting the least and greatest values to the box are called the whiskers. Use the following graph to answer the following questions. This box plot indicates the scores from yesterday’s math test. Approximately what percent of the students did not get above 65%? A. 25% B. 50% C. 65% D. 75% E. 85% The correct answer is Choice (A). The box-and-whisker plot indicates that the lowest score on the test was 60. The median of the lower quartile is 65, so about 25 percent of the students scored lower than 65. It could be exactly 25 percent, depending on the number of students. What is the median test score from yesterday’s math test? A. 25% B. 50% C. 65% D. 75% E. 85% The correct answer is Choice (D). The median of the box-and-whisker plot is indicated by a line drawn through the center of the box. The value graphed at this point is 75. Venn diagrams “Venn” you need to picture relationships between different groups of things, use a Venn diagram. A Venn diagram is an illustration where individual data sets are represented using basic geometry shapes such as ovals, circles, or other shapes. Simply draw and label two or more overlapping circles to represent the sets you’re comparing. The sets overlap in an area called the intersection. When an item is listed in both sets, it goes in the intersection. If an item doesn’t fit in either set, it falls outside the circles or other shapes. Use the following graph to answer the following questions. Football is the favorite sport of how many students in the Venn diagram? A. 2 B. 5 C. 23 D. 25 E. 48 The correct answer is Choice (C). In the Venn diagram, 23 students picked football as their favorite sport. This is the only portion of the diagram reserved for football only. Football and basketball are the favorite sports of how many students? A. 2 B. 5 C. 23 D. 25 E. 48 The correct answer is Choice (B). Five students in the Venn diagram picked football and basketball. This is the portion of the diagram that football and basketball have in common. How many students did not choose football or basketball? A. 2 B. 5 C. 23 D. 25 E. 48 The correct answer is Choice (A). There are two students who did not fall inside the Venn diagram’s circles; therefore, they chose neither football nor basketball. Scramble around scatter plots If you want to determine the strength of your relationship, use a scatter plot. Scatter plots are graphical representations of two variables determining whether a positive, a negative, or no correlation exists. A correlation is a relationship between two variables in which as one increases or decreases, the other one tends to increase or decrease. There is a correlation between time studying and test scores, for example. As time studying increases, test scores tend to increase. Data from two sets are plotted in scatter plots as ordered pairs (x, y). You can draw three conclusions from scatter plots: If the coordinates are close to forming a straight line that rises up from left to right, then a positive relationship or correlation exists. If the coordinates are close to forming a straight line (line of best fit) with one variable increasing as the other decreases, then a negative relationship or correlation exists. If the coordinates don’t come close to forming a line and are all over the place, then no relationship or correlation exists! Hence, the name scatter plot. Here are the three types of correlations: Make sure to give your plot a title and make sure to label your axes when you create a scatter plot. Correlation alone does not prove causation. If a variable tends to increase as another variable increases, for example, it does not mean that the tendency is caused by the other variable. The number of mud puddles tends to become greater when the occurrence of lightning rises. Does an increase in the occurrence of lightning cause the number of mud puddles to get higher? Do the additions of mud puddles cause more lightning? The correlation between the two does not prove that one causes the other, and in fact neither causes the other. An increase in rain causes both. Also, even when a change in one variable does cause a change in another, that alone does not prove which variable change is causing which. Studies have shown that changes in the closeness of the moon cause shifting of the tides, but the correlation by itself is not the proof. If correlation worked that way, we could just as easily conclude that the shifting of the tides causes major changes in the closeness of the moon. Loiter around line plots If you want to see your mode (the value that occurs the most) pop up quickly, use a line plot. A line plot, also known as a dot plot, allows you to identify the range, mode, and outliers in your data set. Follow these simple steps: Put your data in order from least to greatest. Arrange your data on a number line. Mark each value in the data set with an x or a dot. Using the following line plot, determine the mode of the data set. A. 50 B. 60 C. 70 D. 80 E. 90 The correct answer is Choice (E). The score of 90 appears in the data set the most.

View ArticleArticle / Updated 02-24-2020

You improve your chances of choosing the right answer on the Praxis math test — and choosing it quickly — by eliminating choices that you know are wrong. This narrows the set of choices to consider and helps lead you to the right answer. Not only does this increase the probability of getting the right answer, but another advantage is that it helps lead you to better considerations. How to eliminate obviously wrong answer choices If a choice is so outrageous that it couldn’t possibly be the correct answer, you should eliminate it from consideration. For example, the length of a rectangle can never be greater than the rectangle’s perimeter. A person’s age years ago can’t be greater than his or her current age. The mean of a set of data can never be greater than the highest number. These are just some examples of impossibilities you can readily notice. If 3j = 90, what is the value of j? A. 270 B. 30 C. 60 D. 120 E. 3 The correct answer is Choice (B). You can find the answer by solving the equation. To help ensure you get the correct answer, you can eliminate Choices (A) and (D) because both of those choices are greater than 90. You have to multiply 3 by a positive number to get 90, and no positive number is greater than 3 times itself. Eliminating those choices leaves you with three choices to consider instead of five. Choices (C) and (E) are randomly incorrect. The radius of the preceding circle is 12 meters. What is the circumference of the circle? A. 24π meters B. 12π meters C. 12 meters D. 144π meters E. 6π meters The correct answer is Choice (A). The formula for the circumference of a circle is C = 2πr. Substituting 12 m for r, you get 2π(12 m) = 24π m. You can eliminate Choice (C) right away because neither π nor a decimal number, which would result from multiplying 12 by a decimal approximation of π, is in the answer. Another reason Choice (C) can be eliminated is because the radius of a circle can’t possibly equal the circle’s circumference. Multiplying by 2π can never be the same as multiplying by 1; 2π is not equal to 1, and it never will be, as far as we know. Choice (B) can be eliminated because multiplying by π is not the same as multiplying by 2π. You can also eliminate Choice (E) because the number that precedes π in a representation of a circumference can’t be less than its radius unless different units are used. Multiplying a positive number by 2π has to result in an increase. The three eliminations leave you with Choices (A) and (D), and that puts you closer to the right answer. Choice (D) is incorrect because it is the area of the circle, not the circumference, except with m instead of m2. If the unit were m2, you could eliminate it right away because circumference is not properly expressed in square units. Avoid the most common wrong answers Other choices to watch out for and be ready to eliminate are the ones that result from the most common calculation mistakes. Memorizing the rules for all the math topics you’ll face on the Praxis is important for avoiding these common mistakes. For geometry questions, some of the most common mistakes involve getting formulas confused, such as area and circumference. If you have a question about the area or circumference of a circle, you may have an answer choice that gives you the number involved in a measure about which you’re not being asked. Be ready to avoid such answers. Also remember the difference between the interior angle sums of triangles and quadrilaterals. Choices may be the result of using the wrong number. Confusion between supplementary and complementary angles is common, and so is confusion between formulas for surface area and volume. Forgetting the formulas for the volume of pyramids and cones also happens often. As for algebra and number and quantity questions, losing track of the fact that a number is negative is one of the most common mistakes. The distributive property is very frequently used improperly. Remember that the term right before the parentheses is supposed to be multiplied by every term in the parentheses, not just the first one. 5(x + 3) is equal to 5x + 15, not 5x + 3. The rules for switching between decimals and percents can be easily confused. Keep in mind that moving a decimal two places to the right is multiplying by 100 and moving the decimal two places to the left is dividing by 100. Dropping a percent symbol is multiplying by 100 because doing so undoes dividing by 100, and writing a percent symbol is dividing by 100 because a percent symbol means “hundredths,” or “divided by 100.” For statistics and probability questions, be careful about confusing mean, median, and mode. People often forget that the median of a set of data can be found only when the numbers are in order. When using scientific notation, be careful about the direction in which you move decimals. Numbers resulting from wrong decimal directions may be in the choices. Sample questions Which of the following has the same value as 35.937 percent? A. 3,593.7 B. 3.5937 C. 0.35937 D. 35,937 E. 0.035937 The correct answer is Choice (C). To convert a percent to a decimal number, drop the percent symbol, which can be % or the word “percent,” and move the decimal two places to the left. Choice (A) results from dropping the percent symbol and moving the decimal two places to the right. The other choices result from moving the decimal points something other than two places to the right or left. The main lesson here is that Choice (A) can be reached through a very common mistake in converting percents to decimals. You want to avoid such wrong choices. They’re lurking, so be ready. 45 17 90 28 17 What is the median of the preceding set of data? A. 28 B. 90 C. 17 D. 39.4 E. 45 The correct answer is Choice (A). When the numbers are in order, the middle number is 28. It is therefore the median. Interestingly, Choice (A) also happens to be the range of the set of data. Hopefully, you didn’t reach the correct answer because you mistook median for range. Sometimes mistakes lead to the right answers, but we don’t advise counting on that method. Choice (B) is the middle number in the set of data as it is presented, but not when the data is in order. Choice (C) is the mode and the lowest number. Choice (D) is the mean. Choice (E) is just one of the numbers in the set of data.

View ArticleArticle / Updated 02-24-2020

The most unusual thing about the Praxis Core reading test (don’t worry — we said unusual, not difficult) is that it includes what are referred to as visual- and quantitative-information questions, which is the Praxis’s fancy term for questions about charts and graphs. Most reading and writing tests don’t do this. There aren’t a ton of visual- and quantitative-information questions on the Praxis exam. There may only be two or three. Depending on the exam you happen to take, you may see three questions all about the same graph, or you may see one or two questions each about a couple of different graphs. But every point helps, so this section tells you about these questions. Rethink charts and graphs If charts and graphs make you nervous because they seem more like math and science stuff than reading and writing stuff, the first step for you is to think about visual- and numeric-representation questions differently. The fact that visual- and quantitative-information questions are on the Praxis reading portion of the exam isn’t a mistake or the result of someone’s bizarre whim — it proves that, regardless of appearances, these questions really are reading-comprehension questions at heart. A graph — or any kind of picture — can be thought of as a visual depiction of information that could also be presented verbally. Just as you could either compose the sentence “A horse jumps over a fence” or you could draw a picture of a horse jumping over a fence to represent the same idea, a bar graph, line graph, pie chart, or any other type of chart or graph can be thought of as verbal information presented in pictorial form. So, relax. The visual- and quantitative-information questions are reading-comprehension questions. They’re just different. Graphs on the Reading Comprehension Test The most common type of a graph is a line graph. A line graph represents the relationship between two variables: an independent variable plotted along the x (horizontal) axis and a dependent variable (a variable that depends on the first one) plotted along the y (vertical) axis. The line running through the quadrant formed by their intersection is what you look at to figure out what value for one variable is paired with what value for the other. So, say you had a line graph that plotted the relationship between “hours spent studying” and “score on the Praxis reading test” (as though everyone who studied for the same amount of time got the exact same score, which would certainly be nice …). The “hours spent studying” would be plotted with hatch marks along the horizontal axis, and the various possible “scores on the Praxis reading test” would be plotted along the vertical axis, because this is the variable that depends on the other one. If you want to know the score someone who studied for, say, five hours, would get, you’d just proceed upward from the five-hour hatch mark on the bottom until you hit the line representing the actual data, then turn and go left until you hit the corresponding score on the side of the graph. Another type of graph commonly found in Praxis visual- and quantitative-information questions is a bar graph. Rather than depicting the relationship between an independent and a dependent variable like a line graph does, a bar graph represents how different categories stack up against each other with respect to some particular idea. For example, you might use a bar graph to compare the number of World Series won by various baseball teams. The names of all the teams would be plotted along the horizontal with a bar above each name, and the heights of the bars would indicate the number of World Series each team had won, with the vertical axis of the graph hatch-marked to indicate how many championships were represented by a given bar height. The bar representing the New York Yankees would be very high (some might say unfairly high); the bars representing the St. Louis Cardinals, Oakland Athletics, and Boston Red Sox would be lower, but still respectably high; and the San Diego Padres and Texas Rangers wouldn’t have bars over their names at all (at least not as of this writing, since neither team has yet won a World Series). You could also plot that same information with another common type of graph called a pie chart. The difference between a pie chart and a bar graph is that a pie chart represents percentages of a total, so it looks like a circle with different-sized triangle-like pieces marked off inside it (hence its name). On a World Series pie chart, the Yankees’ slice of the pie would be nearly one-fourth of the whole pie, as there have been 115 World Series and the Yankees have won 27 of them. The Cardinals’ slice would be about one-tenth of the pie (11 World Series victories out of 115). Because a pie graph represents percentages of a total, the teams that have never won a World Series wouldn’t appear on the pie at all. But really, there’s no sense in trying to memorize every type of chart or graph in the world. There are far too many ways to represent data visually for it to be in your interest to try and guess which types of charts or graphs will make an appearance when you take the exam. The best approach is to identify key words from the question, connect them to information represented in the graph, and then analyze the answer choices. Sample question Based on the preceding graph, the biggest drop-off in popularity between consecutively ranked pets is between A. the most popular pet and the second most popular pet. B. the second most popular pet and the third most popular pet. C. the third most popular pet and the fourth most popular pet. D. the fourth most popular pet and the fifth most popular pet. E. The drop-offs in popularity between the first and second most popular pets and between the third and fourth most popular pets were equally large. The correct answer is Choice (B). In order to answer this question correctly, you have to think about the pets in order of most popular to least popular — that is, rank them consecutively as the question states. The biggest drop-off in popularity between consecutively ranked pets by a fairly wide margin is between cats (the second-most-popular pet, chosen by 25 students) and fish (the third most popular pet, chosen by about 17 or 18 students), with a drop-off of 7 or 8 votes. Note that the bar graph doesn’t allow you to judge perfectly how many students voted for fish, but that doesn’t matter. Whether fish got 17 or 18 votes, the biggest drop-off in popularity is still between cats and fish. Choice (A) is wrong because cats only got two or three fewer votes than dogs, so this isn’t the biggest drop-off in popularity. Choice (C) is wrong because ferrets only got three or four fewer votes than fish, so this isn’t the biggest drop-off in popularity. Choice (D) is wrong because hamsters only got one or two fewer votes than ferrets, so this isn’t the biggest drop-off in popularity. Choice (E) is wrong because, although it is true that the gap between dogs and cats and the gap between fish and ferrets are equally large, neither of them is the largest drop-off in popularity. It doesn’t matter that they were equally large, because the question was asking for the largest drop-off! Be careful!

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