The post How Many Data Interpretation Questions on the GRE? appeared first on Magoosh GRE Blog.

]]>On the actual test, which has twenty questions per math section, there are only three Data Interpretation questions per section, leading to a total of **six** Data Interpretation questions on the test (not including the experimental section, if it happens to be Data Interpretation).

I know that was a mouthful, so I’m going to simplify things:

1^{st} math section (20 questions total): 3 Data Interpretation questions

2^{nd} math section (20 questions total): 3 Data Interpretation questions

Total number of Data Interpretation questions: 6

Data Interpretation simply means that there is a graph/chart/table and a series of questions relating to graph/chart/table. Each chart/table/graph will have three questions, which is consistent with the above. Meaning, each math section will have one table/chart/graph.

Questions themselves typically draw on percent/fraction/decimal conversion and require some estimation (if you don’t want to fiddle with the calculator). Concepts from statistics, such as mean, median, and mode, also pop up frequently. As to the number of such questions, it is random. The takeaway: know your statistics.

On the Data Interpretation section you may see bar charts, you may see a pie graph, you may see a graph with a bunch of funky lines. You might likely see a combination of such graphs for a set of three problems, and will have to combine information from both graphs to answer a question.

There is, however, no clean breakdown in the types of graph. Your best strategy is to prepare as much as possible, so that you will have exposure to almost every kind of graph permutation that the GRE will throw at you.

There will always be exactly three questions per Data Interpretation set. Each math section will feature exactly one Data Interpretation set. Each set of three questions will pertain to the exact same charts/bars/graphs.

There is no solid breakdown in terms of the type of charts/bars/graphs. So make sure to practice as many variants of the charts/bars/graphs to be ready for test day.

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]]>The post GRE Math: Histograms appeared first on Magoosh GRE Blog.

]]>First, a practice question about the following scenario.

In a survey, 86 high school students were randomly selected and asked how many hours of television they had watched in the previous week. The histogram below displays their answers.

1)

First, a reminder on histograms. Histograms are not simple bar or column charts. A histogram, like a boxplot, shows the distribution of a single quantitative variable. Here, we ask each high school student, “How many hours of TV did you watch last week?”, and each high school student gives us a numerical answer. After interviewing 86 students, we have a list of 86 numbers. The histogram is a way to display visually the distribution of those 86 numbers.

The histogram “chunks” the values into sections that occupy equal ranges of the variable, and it tells how many numbers on the list fall into that particular chunk. For example, the left-most column on this chart has a height of 13: this means, of the 86 students surveyed, 13 of them gave a numerical response somewhere from 1 hr to 5 hrs. Similarly, each bar tells us how many responses were in that particular range of hours of TV watched.

The median is the middle of the list. Here, there is an even number of entries on the list, so the median would be the average of the two middle terms — the average of the 43rd and 44th numbers on the list. We can tell that the first column accounts for the first 13 folks on the list, and that the first two columns account for the first 13 + 35 = 48 folks on the list, so by the time we got to the last person on the list in the second column, we would have already passed the 43rd and 44th entries, which means the median would be somewhere in that second column, somewhere between 6-10.

To calculate the mean, we would have to add up the exact values of all 86 entries on the list, and then divide that sum by 86. In a histogram, we do not have access to exact values: we only know the ranges of numbers — for example, there are seventeen entries between 11 hrs and 15 hrs, but we don’t know exactly how many students said 11 hrs, how many said 12 hrs, etc. Therefore, ** it is impossible to calculate the mean from a histogram**. No one will ask you to do that. No one could reasonably expect you to do that, precisely because it is, in fact, impossible.

If it’s impossible to calculate the mean, then how in tarnation can the GRE expect us to compare the mean to the median? Well, here we need to know a slick little bit of statistical reasoning. Consider the following two lists:

List A = {1, 2, 3, 4, 5}

median = 3 and mean = 3

List B = {1, 2, 3, 4, 100}

median = 3 and mean = 22

In changing from List A to List B, we took the last point and slid it out on the scale from x = 5 to x = 100. We made it an “**outlier**“, that is a point that is noticeably far from the other points. Notice that median didn’t change at all. The median doesn’t care about outliers. The median simply is not affected by outliers. By, contrast, the mean changed substantially, because, unlike the median, **the mean is sensitive to outliers**.

Now, consider a symmetrical distribution of numbers — it could be a perfect Bell Curve, or it could be any other symmetrical distribution. In any symmetrical distribution, the mean equals the median. Now, consider an asymmetrical distribution: if the outliers are yanked out to one side, then the median will stay put, but the mean will be yanked out in the same direction as the outliers. **Outliers pull the mean away from the median**. Therefore, if you simply notice on which side the outliers lie, then you know in which direction the mean was pulled away from the median. That makes it very easy to compare the two. The comparison is purely visual, and involves absolutely no calculations of any sort. (Yes, sometimes you can “do math” simply by looking!)

Having read this, you may want to look at the QC above before reading the solution below.

1) If you think you have to calculate both the median and the mean, then this question would be impossible, since it’s impossible to calculate the mean from a histogram. If you know the trick discussed above, then all we have to notice is that the outliers, the points most distant from the central hump, are at the upper end. They are on the “high side” of the hours scale. The median probably just sits inside that central hump, but the mean has been pulled away from the median in the direction of the outliers, that is, in the direction of the high side of the scale. That means, the mean is higher up on the hours scale than is the median. That means, the mean is greater than the median. Answer = **A**

Notice, this solution involves zero calculations. It is 100% visual.

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]]>The post Boxplots on the GRE appeared first on Magoosh GRE Blog.

]]>Boxplots are one data format you may see on the GRE Data Interpretation questions. First, try these practice questions.

(*The following diagram applies to questions #1-3*)

The following boxplot shows the 2012 season runs batted in (RBIs) of 280 American League batters (the top 280 batters in terms of number of plate appearances).

1) What is the size of the IQR of this distribution?

- 25
- 47
- 56
- 83
- 140

2) How many AL hitters hit more than 25 RBIs in 2012?

- 9
- 56
- 83
- 114
- 140

3) B. J. Upton of the Tampa Bay Rays hit 78 RBIs in 2012; this is the 90th percentile value on this chart. How many players hit between 56 and 78 RBIs?

- 14
- 22
- 28
- 34
- 42

(BTW, that max value of 139 RBIs is Miguel Cabrera, after his extraordinary Triple Crown year.)

In this previous post, I discussed the idea of quartiles and IQR, tools that statisticians use to “chunk” a data set. Sometimes, statisticians add to this the median & minimum & maximum to create something called the “**five-number summary**”

1. maximum

2. third quarter, Q3, the 75th percentile

3. median, 50th percentile

4. first quartile, Q1, the 25th percentile

5. minimum

The beauty of the five-number summary is that it divides the entire data set into quarters — between any two numbers on the five-number summary is exactly 25% of the data.

Because statisticians, like all human beings, are highly visual folks, they created a visual way to display the five-number summary. This visual form is called a **boxplot**. Boxplots were created by the brilliant statistician John Tukey in 1977. The five vertical lines represent the five numbers of the five-number summary, and the “box” in the middle, from Q1 to Q3, represents the IQR, i.e., the middle 50% of the data. Between any two adjacent vertical lines are 25% of the data points.

Here’s an example of a boxplot using real baseball data. The data here are the 2012 season total for strikeouts pitched (by all National League pitchers who pitched at least 75 innings in the season).

Half of all the NL pitchers here pitched between Q1 = 83 and Q3 = 161 strikeouts in the year — these are the pitchers in the IQR, the big blue box in the center. Only 25% of the pitchers in this group struck out fewer than 83 batters— this “bottom 25%” is on the “lower arm”, from 38 to 83. Only 25% of these pitchers struck out more than 161 batters in the 2012 season —- this “top 25%” is on the “upper arm”, from 161 to 230. (BTW, that maximum value, 230 strikeouts, is R. A. Dickey, the knuckleball star pitcher of the NY Mets!) On a Data Interpretation question, ETS could give you a boxplot and expect you to read all the five-number summary information (including percentiles) from it.

If you found the practice questions difficult the first time around, you may want to go back and give them another look, before you read the solutions below.

1) The IQR is the distance from Q1 to Q3. From the boxplot, we read that Q1 = 9 and Q3 = 56, and the difference between them is 56 – 9 = **47**. Answer = **B**

2) From the boxplot, we read that 25 RBIs is the median, so that number divides the list in half. There are 280 hitters on this list: half must be above the median, and half below. Therefore, there are **140** hitters above the median value of 25 RBIs. Answer = **E**.

3) Upton, at 78 RBIs, is the 90th percentile. From the boxplot, we read that 56 RBIs, is Q3, i.e. the 75th percentile. Between the 75th percentile and the 90th percentile is 15% of the list. There are 280 hitters on the list, so 15% of 280 = 0.15*280 = 42. There are **42** hitters between 56 RBIs and 78 RBIs. Answer = **E**.

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]]>The 2^{nd} edition Official Guide has just been released. At the back of the book is a new test (GRE Practice Test 2). In general, the concept break down is not surprising, if you look at the concepts that pop up in Practice Test 1 (which is the same as the practice test in the first edition of the Official Guide).

Word problems abound. There is a fair amount of algebra. Even a few combinatorics problems rear their fearsome heads. And if you’re wondering how many statistics questions are on the GRE, a topic often given scant attention in many prep books – it can pop up in spades. Most interestingly, coordinate geometry only shows up once, and there is not a single rate problem.

The information below pertains to the 50 quantitative questions in Practice Test 2. I have lumped QC and Problem Solving questions together. I have not assigned only one category per question, but have ascribed multiple categories to the same question. For instance, a word problem can contain any number of concepts. To only call it a word problem is a vague. After all ten Word Problems on combinations is very different from ten word problems dealing with percents.

The breakdown of concepts detailed below will likely be very similar to what you see test day. That said you would probably see more than one coordinate geometry question and would probably see a rate question. And just because a concept did not show up on the test, does not mean you will not see that concept test day. Interest problems, both simple and compound, can very well show up.

What is the take away from all this? If you are weak in a certain area, say word problems that deal exclusively with adding a series of numbers, do not fret about this. You may only see one problem, if any, dealing with such a concept. On the other hand, if you are only somewhat comfortable with Statistics it is a good idea to strengthen this area, as you are far more likely to see it test day.

Word Problems (15)

Algebra (9)

Geometry (7)

Statistics (6)

Exponents (5)

Rates (0)

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]]>One category of graph you certainly could see on GRE Data Interpretation questions is the **scatterplot**, and its associated idea of the **best fit line**. Let’s talk about how these beasts operate!

To begin, let’s review scatterplots. When each data point (each person, each car, each company, etc.) gives you a value for two different variables, then you can graph each data point on a scatterplot. Here’s an example. Suppose we survey ten students who came from the same high school to the same college. We ask each student for their total SAT score (M + CR + W) and their GPA in the first semester of their freshman year in college. Each student appears below as a single dot, the location of which shows that student’s SAT score and first semester GPA.

As one would expect, there’s a general “upward” trend: students with higher SAT scores tended to perform better in their freshman year of college. At the same time, there’s some chance variation: right in the middle, three students all scored in the 1700’s on their SATs but, for whatever reasons, had different results in the first semester of their freshman year.

We see there’s a general “upward” pattern to this scatterplot. Suppose we wanted to make a *prediction* based on that pattern. For example, a current high school senior in this high school, planning to attend this same college, would know her SAT score and might be curious about her predicted GPA in her upcoming freshman year of college.

We formalize this pattern by drawing what is sometimes called a “best fit” line. Excel calls this a “trendline.” The official name in Statistics is the Least-Squares Regression Line, but you don’t need to know that. Nor do you need to understand the mathematical details of why this line, as opposed to any other possible line, is in fact the “best fit.”

Here’s the same graph with a best fit line.

The best fit line abstracts a common pattern from the individual data points. The best fit line represents the expected relationship: if we know a new student’s SAT score, then, on average, what would we predict for that student’s first semester college GPA? One student appears almost exactly on the best fit line (sometimes a data point or two will be on the trendline, and sometimes none will be); in this case, we can say that student’s GPA is more or less what we would expect from her SAT score. There are five dots clearly above the best fit line: these five students had higher GPA’s than what we would have predicted from their SAT scores. Four dots are below the line: those four students had first semester GPA’s lower than what we would expect, given their SAT score. Notice that questions of the form “how many individuals had a higher/lower (y-value) than what we would expect from their (x-value)?” are simply asking you to count dots above or below the best fit line.

We also need to make a distinction between people or data used to generate the line, and the new data points predicted by the line. In this case, we used 10 people to generate the best fit line. We have no predictions to make about those 10 people: both their SAT scores and first semester GPA’s are known, now things of the past. If we are asked for the now-completed first semester GPA of the person who had a 1780 SAT score, we look for that dot: that’s the low dot in the middle of the graph, with a value of 2.7 for the GPA (too much first semester partying for that person?) A very different question is: suppose a new person, a high school senior, has a 1780 SAT score and would like to predict her first semester college GPA. For a prediction, we are looking not at any individual point but at the line: the line has a y-coordinate of about 3.2 there, so, on average, we would predict GPA of about 3.2 for this current high school senior.

The past are the dots, the future is the line.

Here’s a practice question to test your understanding of the best fit line: http://gre.magoosh.com/questions/2290

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]]>The post The Basics of Data Interpretation on the GRE appeared first on Magoosh GRE Blog.

]]>**Fact:** within the course of each Quantitative section, you will have, on average, two sets of Data Interpretation questions. Each set will present data in some form (graph, table, etc.), and you will have two or three consecutive questions on that same data set.

Absolutely in the natural sciences, and to a great extent in the social sciences as well, data is king. All scientific authority rests on, or falters in the face of, good scientific data. If you are planning graduate studies in the natural or social sciences, I imagine it’s neither a surprise nor a challenge that the GRE would ask this.

What about the poor crunchy artsy non-techy humanities majors? Yes, it is unfortunate that the general GRE is a one-test-fits-all kind of thing. I would say, though, whether you do science or not, and whatever opinions you may have about science and technology, we all live in a world in which we have been ineluctably affected by science and technology. To that extent, important parameters of our lives have been and will continue to be shaped by the data discovered by scientists. Any intelligent person should have at least basic competency in interpreting the data that can impact our lives. That’s why the GRE asks about it.

Much of this question type is about your ability to read graphs & charts showing data, and really what the GRE is asking is for the most part quite straightforward. The vast majority of these questions revolve around one of the “big five” types of data display:

- Pie Chart
- Column Chart
- Line Chart
- Bar Chart
- Numerical Table

Sometimes, the Data Interpretation set might combine two types — for example, a Pie Chart showing the general breakdown of governmental expenses, and then another chart or table of numbers showing the detail in one category. In rare circumstances, the Data Interpretation might be an entirely different kind of visual information, say, the floorplan of a house, but in those cases, the questions are often particularly simple.

ETS calls a chart a “bar chart” whether the bars are horizontal or vertical. Nevertheless, many sources (such as MGRE) call charts withe horizontal bars “bar charts” and charts with the vertical bars “column charts.” Regardless of the names we use, there is a subtle difference. In general, if the bars represent selected members of a particular category, with no attempt to exhaust the whole categories, and with no particular order among the members, they are represented as horizontal bars, what many folks would call a “bar chart.” For example, if the categories are seven different fruits, seven different makes of car, or seven different nations, those do not nearly exhaust those respective categories, and given the set of seven, there’s no inherent way to order them. (They probably would be listed simply in alphabetical order, for lack of a more meaningful ordering system.) Thus, they would be represented by horizontal bars.

If the categories either have an intrinsic order to them (e.g. various years) or if they represent the full complement of a category (e.g. the three divisions of a corporation), then they would tend to be represented with vertical bars, what many folks would call a “column chart.” Sometimes, column charts are segmented (each bar broken into categories, and sometimes, they are equal height columns where the segments represent percents.

Either variety can have side-by-side bars, if you are displaying two different measurements about each category.

Start looking for data displayed in graphs & charts. Any day’s issue of, say, the *New York Times* is likely to have at least one chart or graph accompanying an article somewhere. That’s even more true for any week’s issue of the *Economist*, arguably the single most intelligent weekly magazine in print. Why does a chart or graph accompany that article? What information is given in the chart that is not given in the article? What aspects of the data does the chart make clear? If you simply can understand what a graph or chart adds to a written article, you are more than well on your way toward mastering GRE Data Interpretation.

Be sure to check out Chris’ post on strategies for Data Interpretation. Below is a sample Data Interpretation for further practice. And, of course, sign up for Magoosh, where we will help you perform better on Data Interpretation and all other types of questions on the GRE.

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]]>The post GRE Data Interpretation Strategies appeared first on Magoosh GRE Blog.

]]>If I had to count the number of questions/concerns regarding combinations or permutations, I’d have to use some pretty mighty factorials to do so. On the other hand, if I had to count the number of times students have expressed the same misgivings regarding Data Interpretation, I’d simply use my hand.

What’s truly surprising is there may be one combination/permutation question or probability question on the test. That’s right—for all those hours students slave away trying to tease out the nuances of these question types, not a single one of these concepts could be covered test day.

What is 100% sure, however, is that you will see a Data Interpretation question. Indeed, over the two math sections you can see as many as eight questions. So make sure you spend a lot of time practicing this question. Below are some helpful tips to get you started.

All of sudden, you are tossed into an unruly world of facts and figures, bars and charts, and pies and lines. The first thing to do—before throwing up your hands in defeat—is to get your bearings. If you see bar graphs, read what is to the side of the bar graphs (the y-axis). Then read the information below the bars. Now you should know what each bar stands for and what it means for one bar to be higher than the other.

At the same time, do not scrutinize the graph. You want to get a sense of the big picture. Once you’ve done so move on to the question. Answering the question will allow you to focus on the relevant information in the passage. Knowing the big picture will allow you to correctly interpret this information.

If you have waded through all the information, determining that you have to find the total dollar amount of exports for Company B, you may be stymied yet. Often ETS gives us unpleasant numbers, like 149,000 and 41%. In fact, we can say the first figure is the dollar amount in thousands of the exports of Companies A – E, and that 39% is the percent of that share attributed to Company B.

Do not whip out the calculator to perform the tedious calculation. Instead, round up 149,000 to 150,000 and round 41% down to 40%. Quick math should give you 60,000. Then find an answer close to 60,000. If in the off chance that there are happen to be two answers very close to 60,000, then use the calculator. However, there will most likely be only one answer close to 60,000.

Sometimes, a graph may not give you an exact dollar amount. Instead, you may only have a bar or a line. Unlike Quantitative Comparison, everything you see in Data Interpretation is drawn according to scale. So if they are asking you for the difference between two bars or points on lines, then use your eyeball. It will save you a lot of time.

Almost every Data Interpretation Set will try to catch you mixing up percent with the actual total. To illustrate: Let’s say that Company X has increased by 40% from 1998 to 2000. Company Y has decreased by 30%. Without knowing the total amount of either company, we cannot say that Company X has more than Company Y.

Don’t just read the tips above—apply them. Hundreds of Data Interpretation questions abound, from those found in Magoosh to those created by ETS.

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]]>The post Save Time on GRE Math — The Power of Approximation appeared first on Magoosh GRE Blog.

]]>Timing is a big issue for many on the GRE math section. One way in which students could end up saving precious minutes is by using mental math shortcuts, the most powerful of which is known as approximation. What I’ve noticed, however, is some students feel they have to set up some sort of proportion to solve a problem, a step that is both tedious and fraught with the potential for arithmetic errors. So, instead of trying to find the exact answer to a problem by furiously crunching numbers on the paper, learn to approximate and avoid running out of time (as well as a case of hand cramps).

When using approximation to solve a problem, either round numbers up or down so that you get a nice, round number to work with. Rounding numbers to the nearest five or zero usually works well. The key to approximating is to make sure the numbers you round to don’t deviate too much from the original numbers.

For instance, let’s take a look at the problem below:

1. What is 49% of 23?

(A) 10

(B) 11.27

(C) 12.8

(D) 13.7

(E) 15

Many students feel the need to set up an equation and solve for an exact value. For the GRE, you do NOT want to do this. Yes, such an injunction may seem counterintuitive, especially for those who vividly recall their high school math days. Whereas getting an exact value usually led to an A in this context, on the GRE an exact value—and the attendant setting up of an equation or proportion—will only slow you down. That is why you want to approximate, or estimate, wherever possible. The gist is to avoid solving the problem. If the answer choices are really close, then, and only then, set up an equation/proportion to get a more exact number.

So let’s take a look at the question above, and let me re-word it. What is 50% of 23? Easy, right? The answer is half of 23, which is 11.5. Notice I rounded up a little bit. But the answer is going to be very close to 11.5. Again, the essence of approximating is to pick a number that is close to any of the numbers and one that is easy to work with. Rounding 23 to 25 still leaves you with a 49. If you also round the 49 to 50, then you start to deviate a little too much from the original problem. With the spread of the answer choices above, you can still get the correct answer by multiplying .50 x 25 and then choosing the closet answer less than your result.

In the end, either approach will yield (C) 11.27. As long as you are able to do mental math quickly, you can make a 1-minute problem a 15-second one. Savvy students may even solve the problem in less time, if they see that when you multiply .49 x 23, the number has to end in a seven. The only answer choice that has a 7 at the end is (C).

Now, if you’re not used to solving in your head, or approximating/estimating in general, my advice is to start with easy problems. Just as importantly, drop that pen or pencil. That’s right—think of the pen(cil) as a crutch that’s only preventing you from walking, so to speak.

Okay, let’s try another type of problem and one you are very likely to see on the data interpretation (this is the section with those pesky pie/bar/curve graphs). Dispensing with the actual graph and winnowing the problem down to its basics, here is an example. And remember—don’t use your pen!

*14% of a company’s inventory shipped. If the company held on to 170,280 items then approximately how many items did they ship?*

*(A) **21,000*

*(B) **22,500*

*(C) **28,000*

*(D) **30,000*

*(E) **32,500*

This problem is much trickier than the first one. To start, we want to note the difference between the items shipped (14%) and the items not shipped (86%). Next, we want to ask ourselves, what’s a nice round number that’s not too far from 86%? What about 80%? Well, look at the answer choices. Notice that they are actually pretty close together. Using 80% for 86% would significantly change the outcome. So let’s try another number closer to 86%. How about 85%.

Now, let’s return to the information in the problem. 170,280 items can be changed to 170,000 items. We can use the 85% to represent the 170,000 items that did not ship. What is the relation between 170,000 and 85%? Notice that 170 is double 85. So, if we double the percent and multiply by 1,000 we get the total number of items that didn’t ship. So, the total number of items that shipped is double 14%, which is 28, multiplied by 1,000, which equals 28,000 (remember the number of items is in thousands, i.e. 170 thousands or 170,000).

Note that the question asks to approximate. 28,000 is not the exact answer but is very close, and hence an approximation. Had we forgotten that we’d approximated in the beginning by changing 86 percent to 85 percent, and thus 14 percent to 15 percent, we could have mistakenly chosen answer 30,000, choice (D).

The takeaway is to solve problems by approximating. Doing so will save you lots of time, while not taxing your brain scribbling tedious math at the margins of your scratch paper. Remember, approximating well takes practice, but once mastered will pay huge dividends in terms of the time saved on the actual exam.

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