Data Analysis, Statistics & Probability
Tackling Graph(ics)
You can think of Graph(ics) items as “Eye and Brain” items. First you use your eyes to find what is needed, then your brain does the rest. Regardless of what the Graph(ics) item specifically asks you to do, always follow this four-step method:
Step 1: Identify the information presented in each graph, chart, or table.
Step 2: Determine what the item wants.
Step 3: Manipulate the graph to find the missing information.
Step 4: Give the item what it wants.
Graph(ics) in Slow Motion
Now let’s look at each step more closely, using a graph we are already familiar with:
4. What two years had the least difference in gross national product?
(A) 1986 and 1990
(B) 1986 and 1988
(C) 1986 and 1987
(D) 1987 and 1989
(E) 1989 and 1990
Step 1: Identify the information.
Look at the bar graph and note what information is being presented to you, both horizontally and vertically. For each year given, there is a bar that denotes the amount of the gross national product. Remember that we are not concerned with what “gross national product” means. We care only about the numbers that represent it. Note that the numbers that represent the gross national product are distributed in increments of 5 and that it is possible to have a negative gross national product.
Step 2: Determine what the item wants.
The item is asking for the least difference between any two years. To put it in everyday language: “What two years are closest to the same amount?” Now that we have a clear understanding of what the item wants, let’s look back to our bar graph. It’s eye time!
Step 3: Manipulate the graph to find the missing information.
There isn’t a whole lot of manipulation with this straightforward graph item, but go ahead and compare the bars in the graph to one another. At first glance, three particular years seem to be relatively close to the same amount: 1986, 1987, and 1989.
On closer inspection of these three years, the smallest difference appears twice. Between 1986 and 1989 there is a difference of 5, and between 1987 and 1989 there is a difference of 5. Write both these answers down and move on to the next step.
Step 4: Give the item what it wants.
It’s not uncommon for the SAT to have more than one correct answer, even on multiple-choice sections, so you need to look at the answer choices and compare them to your answers. Only one, answer choice D, matches your answers. The test-makers are sneaky in that they purposely leave out the other correct answer in order for there to be one legitimately correct answer. Instead of getting all worked up over this, just choose the one answer that matches yours and move on. You gave the item what it wanted, end of story. Put it behind you and focus your attention on the next item.
Guided Practice
Try this item on your own.
14. How many seniors walk to school?
(A) 4
(B) 8
(C) 10
(D) 16
(E) 20
Step 1: Identify the information.
Don’t get overwhelmed because of the multiple graphs and charts. Study each one individually and identify the separate pieces of information presented.
Step 2: Determine what the item wants.
In reading the stem, you’ll find that this item is pretty straightforward.
Step 3: Manipulate the graph to find the missing information.
Remember that the SAT wouldn’t give you two graphs if you needed only one. How do the two charts relate to each another?
Step 4: Give the item what it wants.
Make sure you answer what the item is actually asking for. Distractors are usually numbers that you use to work the solution but are not the correct answer.
Guided Practice: Explanation
Two different graphs and charts? No fear: just use our four-step method to solve this item.
Step 1: Identify the information.
Eye that first pie graph. It shows us the percentage breakdown of how the junior and senior classes get to and from school. It also tells us the total number of students in both classes. The second bar graph displays the actual number of juniors who take the bus, get a ride from their parents, drive, or walk to school.
Step 2: Determine what the item wants.
Fortunately, this item is very direct. We need to find the number of seniors who walk.
Step 3: Manipulate the graph to find the missing information.
From the first graph, we know the percentage of juniors and seniors who walk to school. Now it’s time for your brain to do some of the lifting. Because 10% of juniors and seniors walk and there is a total of 240 juniors and seniors, the actual number of walkers would be .
The second graph only tells us about juniors. But wait: if 20 juniors walk to school, and the total of juniors and seniors who walk is 24, then the number of seniors who walk to school would be: 24 – 20, or 4.
Step 4: Give the item what it wants.
You got this far, now don’t blow it by getting cocky. You know 4 is the right answer, but after staring at the graphs for a few minutes, it would be easy enough to choose C (10) or E (20), because you are familiar with those numbers from solving the problem. You wouldn’t believe the number of students who review their practice tests and say, “I got that right, but I chose the wrong answer.” The only thing the SAT cares about is the bubbled-in answer choice. No partial credit: it’s all or nothing. Be sure to give the item what it wants, answer A.
Independent Practice
Look at the following page when you’ve completed this item.
18. If the seniors who take the bus to school began to carpool with their friends and became part of the population that drove to school, then what would be the approximate percentage of juniors and seniors who drove to school?
(A) 19%
(B) 26%
(C) 32%
(D) 37%
(E) 43%
Independent Practice: Explanation
Step 1: Identify the information.
The first pie graph shows us the percentage breakdown of how the junior and senior classes get to and from school. It also tells us the total number of students in both classes. The second bar graph displays the actual number of juniors who take the bus, get a ride from their parents, drive, or walk to school.
Step 2: Determine what the item wants.
This item is specifically asking you to take the number of seniors who ride the bus and add it to the total number of juniors and seniors who drive. Once this is done, you need to figure out the new percentage of drivers.
Step 3: Manipulate the graph to find the missing information.
First, let’s find the total number of students who take the bus. It is going to be 40% of the total number of juniors and seniors, . From the second graph we know that 80 juniors ride the bus, and if 96 juniors and seniors ride the bus, then the number of seniors who ride the bus is 96 – 80, or 16. This is the number we are going to add to our total number of drivers.
Now we need to do the same thing with the drivers in the first graph that we did with bus riders—find the actual number. . So if there were 60 juniors and seniors driving to school and we added the 16 who used to take the bus, we come up with a new total of 76 drivers.
Step 4: Give the item what it wants.
We are not quite done yet. Remember the item specifically asked for the new percentage of drivers after the bus riders were added to them. So now we need to place our numbers into the percentage formula to get . Note that the question in the item asks for approximate, this simply means to round the answer off some more. That’s answer C, 32%.
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