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 Statistical Analysis Graphs, Charts, and Tables

 Probability Permutations and Combinations
Graphs, Charts, and Tables
Visual data can come in many forms, but the SAT focuses on just three types: graphs, charts, and tables. Think of them as the Big Three. Items containing the Big Three come in one of two flavors: Just Read It Vanilla and Chunky Operations Chocolate.
On these items, the SAT just tests to see whether you understand the data being presented.
There’s nothing controversial or sneaky about these items. The SAT shows you a chart or graph, and you answer a question about the data in the chart or graph. For example:
 5. In the following bar graph, the greatest change in the gross national product of Country Z occurred between which two years? (A) 1985 and 1986 (B) 1986 and 1987 (C) 1987 and 1988 (D) 1988 and 1989 (E) 1989 and 1990
What the heck is “gross national product”? If you don’t know, it really doesn’t matter. All you need to know is that the bars on the graph represent whatever “gross national product” is, and you’re looking for the greatest change between the bars.
A quick look at this graph shows that the three biggest differences appear to be 1987 and 1988, 1988 and 1989, and 1989 and 1990. Because the graph measures the gross national product in increments of 5, you can just count up the amount of change between the years.
• From 1987 (20) to 1988 (–5), there is a difference of 25.
• From 1988 (–5) to 1989 (15), there is a difference of 20.
• From 1989 (15) to 1990 (30), there is a difference of 15.
So the greatest change occurred between 1987 and 1988, choice C.
When dealing with graphs and charts, be sure to pay attention to negative and positive values. Also ignore distracting information—such as the meaning of gross national product—that make easy items seem harder.
Chunky Operations Chocolate
These more difficult items ask you to perform some type of operations on data found in a chart, graph, or table, such as calculating a mean or percent. On these items, just reading the information off the graph isn’t enough. You have to step into the fray and do a little math grunt work. Wear latex gloves if you’re worried about getting your hands dirty, but don’t be squeamish. For example, you might be asked something like this:
 6. What was the percent increase in the gross national product from 1986 to 1987? (A) 1% (B) 50% (C) 75% (D) 100% (E) 125%
First you need to recall the formula for percentage change (check out the Numbers and Operations book in this series if you need a review of percents):
Let’s apply this information to the item. The difference in the gross national product between 1986 (10) and 1987 (20) is 10. Now we divide the difference by the original number. In this case, the original number is 10 (from 1986), the number we increased from to get to 20. So we get:
That’s choice D.
The actual operations you will be performing on the charts and graphs are nothing new, but you will need to be careful when converting the information into mathematical equations.
Double Data Items
The SAT will also require you to interpret and manipulate the data contained in two different graphs or tables. The information you need is going to involve some combination of the graphs and tables.
 9. Approximately what percent of the senior class drives to school? (A) 10.4% (B) 20.8% (C) 25% (D) 40% (E) 55.6%
The basic question is always: how do the data in the two graphs/tables and the information in the stem relate to one another? From the item, we know we need to figure out the total number of seniors, and the total number of seniors who drive to school. From the tables we know:
1. Total number of juniors and seniors, and the percent of juniors and seniors who drive to school
2. Total number of juniors who drive and the total number of juniors in the school
Now we can find the total number of seniors by adding together the number of juniors (80 + 40 + 10 + 20) and subtracting this sum from the number of juniors and seniors (240):
240 – 150 = 90
From graph 1 we can determine the total number of juniors and seniors who drive:
From graph 2 we know that 10 juniors drive to school. Therefore, the number of seniors who drive must be 60 – 10 = 50. Now we have the two pieces of information needed to answer the item. The percent of seniors who drive to school is , or 55.6%. That’s choice E.
Scatterplots
The last type of graph that may appear as an SAT item is the scatterplot graph. This is simply a coordinate graph—you know, those graphs with x- and y-axes—with points scattered all over it.
The dots look like a mess, but there’s a method to the madness. A general pattern should appear, such that the majority of the points appear clustered around a line or a specific point. It’s your job to determine what kind of pattern or trend the points make. You won’t be required to do much more than identify whether the points make up a positive, negative, or zero slope. Here is what a typical scatterplot looks like:
The points are all over the place, but in general they are clustered around the dotted horizontal line.
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