The playlist was created based on a Stanford study that shows that certain types of music engage different areas of the brain and can improve skills such as paying attention, making predictions, and memory.
Check out Wash U’s blog post on Spotify Playlist here.
An Attention Enhancing Study Playlist provided by @WashULaw, an online LL.M Degree
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When the points on a scatterplot lie more or less in a straight-ish line, that is called correlation. When it's a straight line with a positive slope, going up to the right, that's positive correlation, and when it's a negative, slope, that's negative correlation. To say that A and B have a positive correlation is to say that when A goes up, B goes up. Here's an example of a graph with a very strong positive correlation.
Notice, the points are not perfectly in a line, but the upward trend is unmistakably clear. In the real world, examples of variables that are positively correlated are the price of crude oil per barrel & the price of a gallon of gasoline; the number of automobiles in a municipality & the number of traffic lights in that municipality; daily temperature & daily ice cream sales; etc.
Here's another example graph, with a very clear negative correlation.
Again, the points do not line in a perfect straight line, but the downward trend is clear: when the x-axis variable goes up, the y-axis variable does down. In the real word, examples of variables that are approximately negatively correlated are the unemployment rate & the Dow Jones average; the torque of a car's engine & its fuel efficiency; a baseball pitcher's career ERA & his number of career shutouts; etc.
Those two graphs were, by statistical standards, quite "pretty": the pattern is very clear, and little of real-world messiness is evident. Here's some real-world data, exploring that last baseball point: a baseball pitcher's career ERA vs. his number of career shutouts.
This graph only includes career leaders (in the top 1000) in both stats. It's much messier than the previous graphs, which is typical of real world data, but the negative trend is still apparent. BTW, that single dot way up at the top, with Career Shutouts = 110 and a career ERA = 2.17, is the great Walter Johnson, easily one of the finest pitchers of all time.
For the first two graphs, we can easily imagine the straight line that would go through these points and summarize them. It's somewhat less clear exactly where it would lie on the third "messy graph. This line, which summarizes the implicit linear trend in a scatterplot is called alternately a "trend line" or a "line of best fit." The official name in statistics is a "least square regression line", but the exact details about how it is calculated and all its technical properties are well beyond what you need to understand for the GMAT.
Here's the second graph again, with a trendline.
The trend line moves through the center of the linear pattern. Here, the points are negatively correlated, so the trendline has a negative slope.
Here's the baseball graph with its trend line.
The trendline allows us to make prediction of a typical data point. For example, here, if a pitcher has a career ERA of about 3.50, we would expect that pitcher to have, on average, about 20 career shutouts. Pitchers above the trendline had more shutouts than expected for their ERA, and pitchers below the trendline had fewer shutouts than expected for their ERA. Making a predicted y-value for a hypothetical x-value, or judging whether an individual point has a higher or lower "typical" y-value, given its x-value --- this is about all the trendline analysis the GMAT will expect of you.
This caution, about the meaning of correlation, may be more relevant to GMAT Critical Reasoning that it is to Integrated Reasoning. To say A and B are positively correlated is to say: when A is a relatively big number, so is B; and when A is a relatively small number, so is B. A and B "go together." What it does not mean is: A causes B. If A causes B, or if B causes A, then the two variables will have a high correlation, BUT the converse is not true. As the canonical saying in the social sciences goes: correlation does not imply causality. Just because A and B appear together does not necessary mean that A directly causes B or vice versa; it may mean that both are caused by another factor, or there may be a more complex relationship. Inferring causality from correlation is a classic social science mistake: keep an eye out for this in "flawed arguments" on CR questions.
Here's a free practice question involving a scatterplot with a trendline.
1) http://gmat.magoosh.com/questions/2305
This post was written by Mike McGarry, GMAT expert at Magoosh, and originally posted here.
]]>While 54% responded "undecided" to the question “How important will a student’s Integrated Reasoning score be in your evaluation of their overall performance on the GMAT?”, 22% say IR scores will be important, and 24% say IR scores will not be important.
The four question types found in GMAT Integrated Reasoning – table analysis, graphics interpretation, multi-source reasoning and two-party analysis – feature scatter plots, sortable tables, and multi-tabbed data. Such question types, introduced in the new section in June, 2012, are novel compared to the formats traditionally seen on graduate school-level admissions exams such as the GRE, LSAT and MCAT.
Among the major findings:
“Schools generally prefer to gather performance data on a new test or test section before fully incorporating it into their evaluation process,” says Andrew Mitchell, director of pre-business programs at Kaplan Test Prep.
“Not all applicants in 2012 will submit GMAT scores with an IR component," Mitchell adds. "We can expect that, as more data is available, schools will determine clear policies, in which Integrated Reasoning may play a key role. In the meantime, GMAT test takers should not take GMAT Integrated Reasoning any less seriously than the Quantitative or Verbal sections.”
Mitchell notes that because test takers receive a separate score for the Integrated Reasoning section, poor performance can’t be masked by stronger performance on other sections of the test.
***
If you are looking for guidance on your MBA application, Stacy Blackman Consulting can help with hourly and comprehensive consulting services. Contact us to learn more. Visit the website for Stacy Blackman Reviews, and check out the company’s e-publications for more in depth school-by-school guidance.
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Below is a scatterplot on which the individuals are countries. Each dot is a country.
On this graph, the x-axis is the GDP-per-capita of the country. The GDP (Gross Domestic Product) is a measure of the amount of business the country conducts: the size of this depends on both the inherent wealth of the country and the population. When we divide that by the population of the country, we get GDP-per-capita, which is an excellent measure of the average wealth of the country. The y-axis is life-expectancy at birth in that country. The sideways L-shape tells the story: For countries with a GDP-per-capita above $20K, life-expectancy at birth is between 70 and 80 years, but for the poor countries, those with a GDP-per-capita less than about $20K, life-expectancy at birth varies considerably, and is in many cases considerably less than the 70+ years that is standard for most of the world.
Now, as an example of a scatterplot with two different marks on the graph, here the same graph again, with some of the points marked differently.
On this graph, the grey circles are countries on the continent of Africa, and the blue squares are countries in the rest of the world. Notice that essentially, the entire continent of Africa is in the "vertical arm" of the L on the left side, while the rest of the world predominantly makes the "horizontal arm" of the L at the top of the graph. In other words, if you are born in Africa, your odds from birth are far worse than if you are born anywhere else on the planet. The international social justice implications of this are staggering, and well beyond what I can discuss here. This does, at least, give a taste of how the Integrated Reasoning section might ask you to draw a politically or ethically important conclusion from a graph. Suffice it to say: displaying data in a scatterplot can make truly important information visually apparent.
This gets to the heart of why mathematician love graphs, and why the GMAT is likely to give you graphs like scatterplots. A scatterplot makes the relationship between two variables, over a potentially large number of data points, visible at a glance. The more you practice with these graphs, the more you will appreciate their astonishing capacity to convey information in visual form.
Where in the real world might you see scatterplots? As with much of the rest of GMAT Integrated Reasoning material, I highly recommend the New York Times, the Wall Street Journal, and the Economist Magazine as excellent sources that often display complex and highly relevant information in graphical form. Also, here's a Magoosh practice question:
1) http://gmat.magoosh.com/questions/2303
This post was written by Mike McGarry, GMAT expert at Magoosh, and originally posted here.
]]>In this article, I’ll just highlight a few of the things for which I’ll be looking.
This will be my first time sitting for a live IR section. I am curious to see the breakdown by question types (MSR, TA, GI, and 2PA). I know time will be precious on that part: each of the 12 IR “questions” has multiple sub-question parts, and I only have 30 minutes for the whole schmiel, so I will be looking for time-saving tricks I can use in gathering information from graphs and tables. Although a calculator is available, I will probably use it sparingly if at all.
In SC, I’ll be looking for multiple splits among the answer choices. For CR, I will be looking for common CR question types. For the RC, I will make an outline, remembering the strategy: map, don’t memorize! I am curious to see what exotic vocabulary may be used, and what the range of topics is on the sentences and passages.
On DS, I will be looking for ways to answer to the sufficiency question without having to do a full numerical calculation. Throughout the math section, I will be looking for shortcuts (e.g. estimation) that allow me to answer without having to do a long complicated calculation. I am curious about how many data-based questions I will see, given that the IR section is designed for data-based questions.
Perhaps most important will be to go into the exam in the right “head space” – awake and energized, but not stressed or anxious. I will have to get a solid night’s sleep not only the night before, but for a few nights before. I will eat a good dinner the previous night, and a good solid breakfast that morning. I will use my breaks for stretching, and I will try to remember to continue deep breathing even during the test itself.
Any comments? Advice you’d like to give me? Things for which you’d like me to scope out the GMAT? Comment on this post and let me know!
]]>"Rest assured that IR is is new to us, too, and it’s going to take us (and our peer schools) some time before we know how to interpret it as it relates to the Stanford MBA Program," writes Allison Davis.
According to the Graduate Management Admission Council, which administers the GMAT, the new IR section measures test taker's problem-solving skills when presented with data in different formats and from multiple sources.
The section is scored on a scale of 1 to 8 in single-digit increments. Like the Analytical Writing Assessment score, IR will be reported as an independent score that does not affect the computation of the GMAT Total Score.
While schools will see your IR score if you've taken the new GMAT, Stanford GSB says that for this application year, at least, MBA admissions will focus on the verbal, quantitative, AWA and total scores.
Applicants have plenty of things to juggle and worry about throughout their journey to business school, so don't lose a wink of sleep over the new Integrated Reasoning section. We'll have a better idea next year of how the scores play in the evaluation process.
***
If you are looking for guidance on your MBA application, Stacy Blackman Consulting can help with hourly and comprehensive consulting services. Contact us to learn more. Visit the website for Stacy Blackman Reviews, and check out the company’s e-publications for more in depth school-by-school guidance.
]]>Many candidates wonder how the new section will affect their grade and admission chances. And so, a number of the programs are announcing outright that the change is still new to them and they have no way to rate candidates according to the new score.
For example, INSEAD has reported, "Until there is more benchmarking data from test-takers to consider, INSEAD will not be using the IR section to review a candidate’s performance in the GMAT; we will continue to focus on the quantitative and verbal scores as well as the total score."
Stanford has made a similar statement: "For this application year, we will see your IR score if you have taken the new GMAT, but will focus on the verbal, quantitative, AWA, and total scores. Once we have had the chance to review IR scores in this first year, we will determine how to evaluate them in our process for next year."
Kellogg has also admitted that they will continue to base themselves on the quantitative and verbal scores since these are the scores they know and can currently appraise.
It is important to note that candidates who took the older version of the test before June 2012 can still apply with their grades (given of course that the score is still valid), but candidates who took the test as of June 2012 are required to take the new section.
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When GMAC first announced the IR question, it released a few free samples on its own website, but the format was not finalized at that point. Apparently, the 50 IR practice questions on this new website represents the finalized formats of each of the four IR question types, and the level of difficulty of these questions is comparable to what will appear now on IR sections on live GMATs. This post is a summary of what we know about the IR question formats, including what we can glean from these 50 practice questions.
Each IR question is one of four formats: (1) Multi-Source Reasoning (MSR); (2) Table Analysis (TA); (3) Graphics Interpretation (GI); and (4) Two-Part Analysis (2PA). If these are unfamiliar to you, you can read about the basics in the Magoosh IR eBook. On the new website, questions #1-18 are MSR, questions #19-24 are TA, questions #25-34 are GI, and questions #35-50 are 2PA. On this website, they are neatly sorted by question type: we have no idea whether those questions types will be similarly sorted or completely interspersed on the IR section of a live GMAT. We also have no way to guess the relative proportions of each question type to expect on the live GMAT.
We do know: eight of the 12 questions will count, and the other four will be experimental questions. We do know: whatever block of 8 questions counts, those 8 questions will have the same distributions of question for all test takers. We don't know what that distribution is: let's say, just for simplicity, that it's 2 MSR questions, 2 TA questions, 2 GI questions, and 2 2PA questions. That mix will count for everyone. Now, the four experimental questions don't count, so they could be any mix of problems: it could be one of each type, or two of one type and two of another, or all four of a single type. Suppose Fred happens to get an IR section on which all four of the experimental questions are 2PA. In the course of the 12 questions, Fred would see six 2PA questions: if he were counting, he would realize that the experimental questions would have to be 2PA, but think about it. He doesn't start to realize something is unusually until he gets to his 4th or 5th or even 6th 2PA. At that point, he knows some of those 2PA questions had to be experimental, but he has no way of knowing which two count: the first two? the last two? the third and the fifth? Of course, of six questions, there are 6C2 = 15 different ways the two that count could be distributed among them, and all 15 of those scenarios are equally likely. The upshot is: even if you have an inkling that you are getting more of this question than that, you always have to treat the question in front of you as if it counts.
Also, let's talk a little about this word "question" --- we say the website has 50 practice "questions" and the IR section has 12 "questions", but I would argue a more accurate term would be "screens." The website has 50 screens, and the IR section of the GMAT has 12 screens. Each screen will be one of four formats --- MSR, TA, GI, 2PA --- and almost every screen has more than one question on it. Rather than talk about how many questions within each question, for clarity, for the remainder of this post, I will refer to each "screen" and how many questions on that screen. Here's a little of what we can glean about the four screen formats from the 50 IR practice screens on the website.
This is the only of the four types in which the same content appears across multiple screens. For every other question format, all the relevant content appears on one screen, and none of that content appears on any other screen. Some MSR screens have a single five-choice multiple choice (MC) question: on the whole IR section, this is the only screen type, the only question type, on which there is only one question on the screen. The others, in fact, the majority of MSR screens, have Multiple-Dichotomous Choice (MDC) questions: each MDC screen had three individual MDC questions.
On the 18 screens devoted to MSR, there were four different prompts, and multiple screens for each prompt. Here's the breakdown:
Prompt |
screens |
# MDC |
#MC |
hotels for a conference |
#1-6 |
4 |
2 |
the Nairobi Stock Exchange |
#7-9 |
2 |
1 |
sports & broadcasting rights |
#10-12 |
2 |
1 |
WHO study of the growth of children |
#13-18 |
4 |
2 |
As we can see, the ratio of MDC to MC is 2:1, which makes me strongly suspect that something like this will be the ratio on the live GMAT: certainly, expect more MDC than MC. A bank of six screens on a single topic might be a little excessive: after all, that would be half the IR section right there. I would think of this like the long RC passage in the OG that have, say 6 questions: no RC passage on the live GMAT will have 6 questions, but we get the extra questions in the OG for additional focused practice. Similarly, here, with extra MSR screens.
All MSR prompts had two cards: none had three cards, so apparently this is the standard. The first and second prompts each involve one card with text and one with a table. The third prompt has nothing but text on both cards. The fourth prompt has text + a table on the first card and text + a graph on the second card. This is the "integrated" part of IR: integrating mathematical information with verbal information. While an "all-text" MSR prompt (like the third one here) may appear, apparently the majority of MSR prompts will involve tables or graphs as well as text.
Few surprises here. Each TA screen contains a verbal prompt and a sortable table. Most of the tables have 7-8 columns, but one had 5 columns and one had 6 columns. On each TA screen, there are 3 MDC questions.
Each GI screen presents a verbal prompt and a graph. The questions on a GI screen are in the form of two drop-down menus in a fill-in-the-blank format. That is to say, underneath the graph will be one or two sentences, with a total of two blanks: the student "fills in" the blank with a choice from the drop-down menu: most of the drop-down menus have 4 choices, although some had 3 choices, and a few had 5 choices. Here are the graphs that appeared:
#25 = a column chart (i.e. a histogram)
#26 = a pie chart
#27 = double-sided* scatterplot
#28 = a clustered column chart
#29 = scatterplot with two different populations
#30 = three timeplots on the same graph
#31 = double-sided* column chart
#32 = segmented column charts
#33 = four timeplots on the same graph
#34 = a clustered column chart
For more on column charts, clustered column charts, and segmented column charts, see this post. It's reasonably clear that they love their column charts!
By "double-sided", what mean is: there are two y-axis scales, one on the left side of the graph, and another on the right side of the graph. For example on screen #27, there are orange dots and black squares on the scatterplot: the orange dots are read on the left y-axis scale, and the black squares are read on the right y-axis scale. It's a slick way of showing the interrelationship of three different variables.
In some ways, 2PA is the most flexible of the four question formats. Individual 2PA screens can be purely verbal (similar to RC and CR questions) or mathematical. This table summarizes these 16 screens according to type and number of answer choices (#A), with some comment on the nature of the "two parts" of the question. Here are my codes for the 2PA screen types:
V = completely verbal
MA = mathematical, with algebraic/variable answer choices
MN = mathematical, with numerical answer choices
Screen |
Type |
#A |
Comments |
#35 |
V |
6 |
one true, one false |
#36 |
MN |
5 |
scenario links the numbers needed |
#37 |
V |
5 |
one cause, one effect |
#38 |
MN |
5 |
scenario links the numbers needed |
#39 |
V |
6 |
assumption required, possible fact |
#40 |
MN |
6 |
largely a verbal question, describing a corporate hierarchy, and the question is about how many people would be involved in different review processes |
#41 |
V |
5 |
a characteristic of pottery, and a prediction possible about group that made the pottery |
#42 |
MA |
6 |
a geometry problem |
#43 |
V |
6 |
two academics disagree: the two parts play into this disagreement. |
#44 |
MN |
5 |
a distance-rate-time problem |
#45 |
V |
5 |
one cause, one effect |
#46 |
MN |
5 |
two terms of a recursive series |
#47 |
V |
5 |
most strengthen, most weaken |
#48 |
V |
5 |
penalties for missed work time, which merits a verbal reprimand, which merits a written reprimand |
#49 |
V |
5 |
a ballet company, what will decrease expenses? increase audience size? |
#50 |
V |
5 |
advertising in two cities, what should be done in each city to test a hypothesis? |
Of these 16 questions, 10 are verbal and 6 are mathematical in some way. I would take that as an indication of the relative proportions of verbal 2PA screens to mathematical 2PA screens. All have either 5 or 6 choices, and the skills required vary from RC & CR skills on the verbal types to assorted Quantitative skills on the mathematical type.
This analysis of the 50 practice IR questions on gives us a much more precise idea of what to expect on the real GMAT. Read the Magoosh IR eBook, study this post, work through the 50 questions on the GMAC IR website, and practice the Magoosh IR questions ---- if you do all that, you will be well-prepared for your 12 IR screens on test day.
This post was written by Mike McGarry, GMAT expert at Magoosh and originally posted here.
]]>Kaplan has the resources you need to succeed on the updated exam.
The GMAT has changed this month — and Kaplan is here to make sure you're ready to take on the new test. The updated GMAT features a slightly tweaked exam structure and a brand new section, Integrated Reasoning, which introduces four new question types and a separate score. What this means for you is more hours of studying if you want to achieve a competitive score.
Kaplan's GMAT courses include a dedicated Integrated Reasoning session and full-length IR test sections for all 9 CATs included in the program. We've worked with GMAC, the test maker, to ensure you have everything you need to prepare for the new test. We've also put the latest news, new practice questions and helpful resources in our GMAT 2012 Test Change Info Center, testchange.com, your hub for all things related to the new exam.
You're facing a tougher road to an elite score, but Kaplan knows the way to get you there. Visit us to see what's new with the GMAT and learn more about our programs.
Warm Regards,
The team at Kaplan GMAT
In terms of foundations skills, what you need to know for Integrated Reasoning is not really different from what you need to know for the Q & V sections. You need to know basic math, especially percents and ratios, and you need to be able to interpret word problems. You need to know how to read graphs. You need to read critically and interpret, much as you do on CR and RC questions. These are the basic skills absolutely required to negotiate the IR section, but they are not really what the IR is designed to test.
The IR section is designed to assess higher order reasoning. These skills include:
1) Integrating information, including organizing and synthesizing different kinds of information.
2) Evaluating sources of information, or evaluating tradeoffs and possible outcomes of a course of action.
3) Drawing inferences, making predictions, identifying what further conclusions are supported by the given data.
4) Interrelating information, seeing how parts fit together in context
5) Formulating strategy, deciding among possible plans of action
These are all skills that managers need for success in the business world. These are skills that business school professors reinforce and assess. This is precisely why hundreds of business school faculty from around the world provided GMAC with the feedback that lead to the creation of the IR section.
Yes, there are challenges associated with the new IR section. Ultimately, the challenges of the IR section are closely related to the challenges you will experience in business school and as a manager in the business world. These challenges, these opportunities to apply your creativity and insight to complex problems, are part of what make the business world engaging, even exhilarating, for folks. This is the exciting world you are entering, and it starts for real when you sit for the "next generation" GMAT and face the IR section. Do everything you can to prepare, so that when you face the IR section, you can bring your best to the challenge.
How to prepare? Sign up for Magoosh, and we will help you be the best you can be on test day.
This post was written by Mike McGarry, GMAT expert at Magoosh, and originally posted here.
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