Chapter 23

Deciphering Data in Charts and Graphs

IN THIS CHAPTER

Taking a five-step approach to integrated reasoning questions

Tackling tables to get the data you need

Getting a grasp on bar and line graphs

Circles and more circles: Pie charts and Venn diagrams

Not every integrated reasoning question relies on a chart or graph, but most do. This chapter reviews the characteristics of the ways the GMAT represents data in the integrated reasoning section and explains how to read each type in the most efficient way.

The charts and graphs you’ll encounter on the GMAT integrated reasoning section display data in a variety of formats. You interpret the data provided in tables, bar graphs, line graphs, scatter plots, pie charts, or Venn diagrams, and then you apply your analysis to draw conclusions about a bunch of scenarios. You get to compare statistics, identify trends or lapses in trends, make predictions for the future, and so on.

Approaching Integrated Reasoning Data in Five Easy Steps

Most integrated reasoning questions contain a chart or graph. You won’t have much time to waste, so it’s a good idea to know how to extract data from the various types of charts and graphs before you sit down in front of the computer on exam day. Regardless of the graph or chart you’re working with, you’ll follow a similar, five-step approach:

1. Identify the type of chart or graph.

   Graphs display data in different ways, so start by recognizing which graph or chart type you’re dealing with. To make this step easy, we provide detailed information on each of the most common charts and graphs on the GMAT in this chapter.

2. Read the accompanying question and determine what it asks.

   Before you attempt to read the chart or graph, examine the question to figure out exactly what kind of information you need to answer it.

3. Isolate what you need to get out of the chart or graph to successfully answer the question.

   Refer to the chart or graph to discover where it conveys the specific data you need to answer the question.

4. Read the chart or graph properly.

   Examine the chart or graph carefully to spot trends and note where the quantities associated with each variable appear and how the value of each increment is displayed.

5. Solve the problem.

   Use the data you’ve carefully extracted from the chart or graph to come up with the correct answer to the question.

The remaining sections in this chapter show you how to apply this approach to reading a variety of charts and graphs.

Translating Information in Tables

Tables report, organize, and summarize data and allow you to view and analyze precise values. For example, a table can be an effective way of presenting average daily high and low temperatures in a given area, the number of male and female births that occur each year within a population, or the ranking of a band’s top-ten hits.

The sample table in Figure 23-1 records the four individual event and all-around scores for five gymnasts in a local meet. Its data is precise rather than approximated, which allows you to come up with accurate analyses of the values. For example, you can see from the table that Kate just barely edged out Jess on the balance beam by a 0.005 difference in scores.

© John Wiley & Sons, Inc.

FIGURE 23-1: You’re likely to see a table like this one as part of a GMAT integrated reasoning question.

When you evaluate a table, pay particular attention to the column labels to determine exactly what kind of information and values it displays. Read carefully to differentiate values and determine, say, whether the numbers represent percentages or actual figures. For example, a few seconds of careful consideration of the values in the sample table in Figure 23-1 tells you that the gymnasts’ all-around score is the sum of the other scores rather than their average. So if a question asked you about a particular gymnast’s average score for all events, you’d know you’d have to compute this calculation rather than report the provided all-around score.

Not surprisingly, tables are the primary source of information in the integrated reasoning table analysis question type. These questions use tables to display data, usually a lot of it. You may also find tables in multi-source reasoning and two-part analysis questions. (Chapter 22 provides more details on how to answer all four integrated reasoning question types.)

Making Comparisons with Bar Graphs

Bar graphs (also sometimes called bar charts) have a variety of uses. They’re especially good for comparing data and approximating values. As the name suggests, they use rectangular bars to represent different categories of data (either horizontally or vertically); the height or length of each bar indicates the corresponding quantity for that category of data.

You see bar graphs most frequently on the GMAT in graphics interpretation questions, but they may also appear in multi-source reasoning and two-part analysis questions. Simple bar graphs present the relationship between two variables. More complex bar graphs show additional data by displaying additional bars or by segmenting each individual bar. We show you how to read simple and complex bar graphs in the following sections.

Simple bar graphs

Bar graphs provide an excellent way to visualize the similarities and differences among several categories of data. Even a simple bar graph, such as the one in Figure 23-2, can convey a whole bunch of information.

© John Wiley & Sons, Inc.

FIGURE 23-2: Simple bar graph.

The chart heading in Figure 23-2 defines the overall category of information: 2009 activity ticket sales for Pleasantdale High School by group. You don’t need a title for the horizontal axis. It’s obvious from the chart heading that each bar provides the data for each school group. From the vertical axis title, you discover that the data represents number of tickets sold rather than the total revenue from those tickets. In Thousands means that each major horizontal gridline represents 1,000 tickets. Each of the four minor gridlines between each major gridline represents 200 tickets (the four lines divide the segments between the whole number into five parts, and ). So the graph indicates that the number of drama club tickets sold was approximately 3,700 because the Drama Club bar ends between the third and fourth minor gridlines above the 3,000 mark. To find the total number of drama club tickets sold, add 200 for each of the three minor gridlines and half of that (100) as represented by the half space between the third and fourth minor gridlines: .

Some GMAT bar graphs may display information for a range of values. An example appears in Figure 23-3. Based on this graph, you can figure that the minimum total number of tickets sold by all groups in 2009 was the sum of the lowest number for each group (), or 15,000 tickets. The maximum possible total of tickets sold by the three groups combined was the sum of the highest value for each category: , or 18,000.

© John Wiley & Sons, Inc.

FIGURE 23-3: Simple bar graph showing ranges of values.

Graphs with many bars

Altering the design of a bar graph allows you to convey even more information. Graphs with multiple bars reveal data for additional categories. For example, Figure 23-4 compares the ticket sales totals for the three groups by year for three years.

The legend designates which group the bars stand for. This graph allows you to easily make comparisons over the years and among the three groups. For example, it’s easy to see that in 2009, glee club ticket sales were not only greater than they had been in previous years but also exceeded sales for either of the other two groups. Perhaps sales were influenced by the launch of a popular TV show featuring a high school glee club!

Segmented bar graphs

Graphs with segmented bars display the characteristics of subcategories. Each bar is divided into segments that represent different subgroups. The height of each segment within a bar represents the value associated with that particular subgroup. For example, Pleasantdale High can provide more specific comparisons of the ticket sales during different times of the year by using a segmented bar graph, such as the one in Figure 23-5.

© John Wiley & Sons, Inc.

FIGURE 23-4: Bar graph with multiple categories.

© John Wiley & Sons, Inc.

FIGURE 23-5: Segmented bar graph with subcategories.

You apply subtraction to read a segmented graph. The top of each bar is the total from which you subtract the designations for each subcategory. So for the Football Team bar in Figure 23-5, the total number of tickets sold in 2009 was 4,500. The number of tickets sold in the fall is represented by the lower segment, which climbs up to about the 4,000 mark. The number of tickets sold in the spring is the difference between the approximate total number of tickets (4,500) and the approximate number of fall tickets (4,000), which is about 500. The graph also reveals that activity sales for the glee club and drama club occur more consistently across both seasons than for the football team, which sells many more tickets in the fall than it does in the spring.

Whenever you reference data from a bar graph, you speak in estimates. Bar graphs don’t provide exact values; that’s not their job. They allow you to make comparisons based on approximations.

Evaluating Line Graphs

Another graph that crops up frequently in GMAT graphics interpretation questions is the line graph. Line graphs display information that occurs over time or across graduated measurements and are particularly effective in highlighting trends, peaks, or lows. Typically (but not always), the x-axis displays units of time or measurement (the independent variable), and the y-axis presents the data that’s being measured (the dependent variable).

Basic line graphs

The line graph in Figure 23-6 shows the garbage production for three cities for each of the four quarters of 2011. You can tell from the graph that Plainfield produced more garbage in every quarter than the other two cities did, and it’s evident that all three cities produced less garbage in Quarter 3 than they did in the other quarters.

© John Wiley & Sons, Inc.

FIGURE 23-6: Line graph.

Scatter plots

Line graphs are extensions of scatter graphs, or scatter plots, which display the relationship between two numerical variables. These graphs display a bunch of points that show the relationship between two variables, one represented on the x-axis and the other on the y-axis. For example, the scatter plot in Figure 23-7 plots each city’s population on the x-axis and its garbage production on the y-axis. Scatter plots show you trends and patterns. From Figure 23-7, you can figure out that, generally, a direct or positive relationship exists between a city’s population and the amount of garbage it produces. The graph indicates that this is the case because the data points tend to be higher on the y-axis as they move to the right (or increase) on the x-axis. You can also surmise that of the 20 cities listed, more have fewer than 200,000 people than have greater than 200,000 people. That’s because the graph shows a greater number of points that fall to the left of the 200,000 population line than to the right.

© John Wiley & Sons, Inc.

FIGURE 23-7: Scatter plot or scatter graph.

Scatter plots also convey trend and pattern deviations. The GMAT may provide a scatter plot with or without a trend line. The trend line shows the overall pattern of the data plots and reveals deviations. The scatter plot in Figure 23-7 doesn’t display a trend line, so you have to imagine one. You can lay your noteboard along the graph to help you envision the trend line if one isn’t provided. Figure 23-8 shows you the trend line for the garbage production graph. With the trend line in place, you can more easily recognize that the largest city in the county deviates from the trend somewhat considerably. Its garbage production is less in proportion to its population than that of most other cities in the county. You know that because its data point is considerably below the trend line.

© John Wiley & Sons, Inc.

FIGURE 23-8: Scatter plot with trend line.

Complex scatter plots

Sometimes the GMAT crams even more information on a scatter plot by introducing another variable associated with the data. The values for this variable appear on the y-axis on the right side of the graph. This type of graph is just a way of combining information in one graph that could appear on two separate graphs.

Figure 23-9 shows you an example of a complex scatter plot. It adds another variable (average yearly income by population) to the mix. The average annual income for each city lies on the y-axis. The points for one set of data have different symbols than those for the other so that you can distinguish between the two sets. The legend at the right of the graph in Figure 23-9 tells you that garbage production is represented by diamonds, and the symbol for income is a square. The trend line for the relationship between city population and average yearly income has a negative slope, which shows you that the smaller the population, the greater the average yearly income. This trend indicates an inverse relationship between city population and average yearly income.

© John Wiley & Sons, Inc.

FIGURE 23-9: Scatter plot with multiple variables.

The GMAT may ask you to identify the relationship between two variables as positive, negative, or neutral. If the trend line has a positive slope, the relationship is positive; if it has a negative slope, the relationship is negative. If the trend line is horizontal or the points are scattered without any recognizable pattern, the relationship is neutral, meaning that no correlation exists between the variables.

When you encounter scatter plots and line graphs with more than two variables, make sure you keep your variables straight. So if you’re asked a question about garbage production, using Figure 23-9, you have to use the data represented by the left vertical axis and the diamond symbol rather than the right axis and the squares.

Like bar graphs, line graphs display approximate values. Use the technique explained in the earlier section, “Simple bar graphs,” to help you estimate the values associated with each data point from the axes labels and grid marks on these graphs.

Clarifying Circle Graphs (also Known as Pie Charts)

Circle graphs, also known as pie charts, show values that are part of a larger whole, such as percentages. The graphs contain divisions called sectors, which divide the circle into portions that are proportional to the quantity each represents as part of the whole 360-degree circle. Each sector becomes a piece of the pie; you get information and compare values by examining the pieces in relation to each other and to the whole pie.

When a graphics interpretation question provides you with a circle graph and designates the percentage values of each of its sectors, you can use it to figure out actual quantities. The circle graph in Figure 23-10 tells you that Plainfield has more Republican affiliates than Democrat and that Democrats constitute just over twice as many Plainfield residents as Independents do.

© John Wiley & Sons, Inc.

FIGURE 23-10: Circle graph or pie chart.

When you know one of the quantities in a circle graph, you can find the value of other quantities. For example, if a multi-source reasoning question in the integrated reasoning section provides you with both the scatter plot in Figure 23-7 and the circle graph in Figure 23-10 and tells you that the city of Plainfield was the city in Figure 23-7 with the highest population, you can use information from both graphs to discover the approximate number of Plainfield residents who are registered Democrats. The city with the largest population in Figure 23-7 has around 500,000 residents. Figure 23-10 tells you that 32 percent of Plainfield residents are Democrats. So just about 160,000 () Democrats reside in Plainfield.

Extracting Data from Venn Diagrams

Venn diagrams, such as the one in Figure 23-11, are made of interconnected circles — usually two or three — and are a great way to show relationships that exist between sets of data. Each data set is represented by a circle; the interaction of the circles shows how the data relates.

© John Wiley & Sons, Inc.

FIGURE 23-11: Venn diagram of 100 cat and dog owners.

You see Venn diagrams most often in graphics-interpretation questions. For example, the GMAT could tell you that the Venn diagram in Figure 23-11 represents the results of a survey of 100 cat and dog owners. You know from the diagram that 33 of those surveyed own cats, but no value appears for the number of dog owners. The shaded portion represents the intersection: the four members of the survey who own both cats and dogs. If you need to find the number of those surveyed who own dogs, you can’t simply subtract 33 from 100 because that doesn’t take into consideration the four people who own both types of pets. The total number of people in the survey who own dogs is actually (100 – 33) + 4, or 71. The number of people in the survey who own dogs only, and not cats, is 71 – 4, or 67.

Your calculations can get a little more complicated when not all the members of the general set are represented by the circles in the Venn diagram. For example, say the survey represented in Figure 23-11 was modified a bit to represent 100 pet owners instead of 100 cat and dog owners. The 100 members of the survey could own cats, dogs, or other pets. The results of this survey appear in Figure 23-12.

© John Wiley & Sons, Inc.

FIGURE 23-12: Venn diagram of 100 pet owners.

Based on this diagram, the GMAT could pose questions that ask for the number of people who own only cats but not dogs, the number of people who own at least one cat or one dog, or the number of those surveyed who own neither a cat nor a dog. Here’s how you’d solve for these three cases:

• The number of pet owners who own cats but not dogs is simply the quantity in the cat-owner circle that doesn’t include the number in the intersection of the two circles. Of the 100 people surveyed, 29 own cats but don’t own dogs.
• The total number of cat owners is 33, which is what you get when you add the 4 cat and dog owners to the 29 owners of cats but not dogs. To find how many of the surveyed pet owners own at least a cat or a dog, you just need to add the values in each circle and add the quantity in the shaded intersection: . Of the 100 people surveyed, 98 owned at least one cat or one dog.
• Figuring the number of pet owners who own neither a cat nor a dog means that you’re looking for the quantity that exists outside of the two circles. The number of pet owners represented inside the circles plus the number of pet owners outside of the circles is equal to 100, the total number of pet owners surveyed. You know the number of people represented by the space inside the circle; it’s the same number as those who own at least a cat or a dog (98). The number of pet owners who don’t have a cat or a dog is simply 100 – 98 or 2.

So to evaluate Venn diagrams correctly, keep track of the total members in the set and what they represent. Information in the question will allow you to assess whether the circles represent the total number of members or whether a subset of members resides outside of the circle, so reading carefully will allow you to accurately interpret the Venn diagram. When you’ve successfully figured out the general set and the subsets, extracting information from Venn diagrams is easy.