**SAT Math: Charts and Graphs Questions**

One of the SAT’s biggest goals is to measure students’ abilities for future success.

For this reason, the SAT doesn’t *just* test content you’ve learned in high school. It also tests what you need to succeed in college, such as critical thinking skills and logical reasoning.

The SAT, for example, incorporates many charts and graphs questions that challenge students to interpret data on their own. In fact, charts and graphs appear on all required sections of the test!

Unsurprisingly, these figures are especially prevalent on both SAT math sections, which are very interested in students’ data analysis skills.

Such graphs might look overwhelming at first, particularly for students who haven’t done much data analysis in high school. But these questions are much easier if you know exactly what the SAT is looking for.

Here’s what we cover in this post:

## Reading SAT Graphs Successfully

Both SAT Math sections (No-Calculator and Calculator) include a significant number of charts and graphs questions. These questions often include a figure and require students to perform basic data analysis.

Fortunately, these questions usually don’t require too much calculation beyond simple arithmetic. For this reason, they should actually be some of the easiest on the test, as long as you understand what you’re looking at.

We discuss strategies for approaching Charts and Graphs questions in a recent post.

When it comes to SAT Math data analysis questions, it’s always vital to identify some key information about a chart or graph before plunging into the question.

For example, we encourage students to ask the following questions when looking at an SAT graph:

- What is the
**title**of the chart or graph? - If it’s a graph, is there a key? What are the labels on the axes? What are the units?
- Make sure to pay extra attention to the
**units**on the axes, as many incorrect answers will be off by a factor of 10

- Make sure to pay extra attention to the
- What is the general trend/shape of the graph?
- Is the relationship linear? Is it exponential?

- Are there any
**outliers**? How do they affect the overall data set? - Note how data is
**clustered**.- Is it very spread out? Centered around the mean?

- If the graph is a line, ask yourself what the
**slope**is.- Slope is always rise over run (change in y vs. change in x), and the unit of the slope will also correspond to the unit on the y-axis divided by the unit on the x-axis

- If there are a
**pair of lines**in a chart, notice where the greatest points of similarity/difference between the lines are

You won’t necessarily have to ask *all *of these questions when engaging with an SAT chart or graph. However, these questions encourage students to consider the graph in context before identifying the task itself.

## Types of SAT Math Charts and Graphs Questions

It’s worth noting that students shouldn’t expect to see an even distribution of graphs/charts throughout the math sections.

The Calculator Section (Section 4) tends to be much heavier on Data Analysis & Problem Solving, and so you can expect to see most graphics in the latter portion of the test.

What kinds of charts and graphs appear on SAT Math?

Students can expect to see problems involving:

- Scatterplots
- Bar Graphs/Histograms
- Line Charts
- Two-Way Tables

We do want to note that students can expect to encounter many Cartesian graph questions testing algebraic principles like slope, slope-intercept form, midpoints, and distance formula. As these require extensive outside content knowledge to answer, we will not address these in this post.

Let’s look at some of these common graph types in more detail below.

## Scatterplots on SAT Math

Scatterplots are an important tool in statistics. An important function of statistics is its ability to predict values based on a limited amount of data, and scatterplots help us to do just that.

In a scatterplot, each individual point on the graph represents a **real point of data. **

A **line of best fit **is then drawn through those points to represent the approximate trend of those values. We can then use that line to predict values outside of the tested range.

For SAT Math, you should understand the following about scatterplots:

- The further a point is from the line of best fit, the more likely it is to be an
**outlier** - You can extend the line of best fit to
**predict future values** - The line of best fit is an
**estimate**, which means we cannot determine definitive values off of the line - The
**slope**of the line of best fit represents the predicted increase (or decrease) in y for each unit increase of x - The
**y-intercept**is the value of*y*when the x-value is 0

Let’s look at an example of a question involving a scatterplot:

**How to solve:**

In the scatterplot, each individual point represents a recorded heart rate at a given swim time. The line of best fit provides the predicted heart rate for the set of times. The question asks us to determine the difference between the predicted heart rate at 34 minutes and the actual heart rate at 34 minutes.

We can see that at 34 minutes, Michael’s actual recorded heart rate was 148 BPM, and the line of best fit predicts a heart rate of 150 BPM. The difference, therefore, is 2, oranswer choice B.

## Bar Graphs / Histograms

Another common type of SAT Math graph is the bar graph or histogram. Bar graphs are used to show the frequency with which different variables occur within a data set.

Bars of differing heights reflect the relative frequencies of each variable.

For example, a *taller *bar indicates a higher frequency of that piece of data. A *shorter *bar indicates a lower frequency of that piece of data.

When approaching a bar graph, be sure to pay attention to the following:

- The
**title**of the graph, which will identify the type of data set - The
**variable(s)**listed along the**x-axis** - The
**frequencies**measured along the**y-axis**

Let’s look at an example:

**How to solve:**

As mentioned, the x-axis on a histogram will list the different items measured, while the y-axis will list the frequency with which each item occurs.

In this histogram, the x-axis lists the different number of seeds in each of 12 apples.

Based on the graph, we can conclude that2 apples had 3 seeds, 4 apples had 5 seeds, 1 apple had 6 seeds, 2 apples had 7 seeds, and 3 apples had 9 seeds.

To find the average number of seeds per apple, we simply need to add up the total number of seeds and divide by the total number of apples. To find the total number of seeds, we multiply the different number of seeds along the x-axis by their respective frequencies, and then add those values together. In other words:

Total seeds = (2 apples x 3 seeds) + (4 apples x 5 seeds) + (1 apple x 6 seeds) + (2 apples x 7 seeds) + (3 apples x 9 seeds) = 73 seeds

We then divide that value by the total number of apples, which is 12.

73 seeds/12 apples = 6.08, which is closest toChoice C.

## Line Graphs on SAT Math

Line graphs are used to show how the relationship between two variables changes over time. Like a bar graph, the title of a line graph on SAT Math usually describes this relationship.

For example, a line graph may be titled “Number of SAT prep companies in the U.S. from 2000 to 2020” or “Percentage of students who graduated high school in New Jersey between 1992 and 1997.”

In the case of line graphs:

- The
**x-axis**will list the**independent variable** - The
**y-axis**will list the**dependent variable**

Often, the x-axis will designate a given time frame, such as years or hours. Pay careful attention to units when analyzing a line graph, as it can be easy to gloss over these (and lose precious points)!

Let’s look at an example of an SAT line graph question:

**How to solve:**

In this line graph, the y-axis marks the number of millions of portable media players sold worldwide. The x-axis lists each year sales were measured (between 2006 and 2011).

First, we need to determine how many portable media players were sold in 2008. If we go over to 2008 on the x-axis, we can see that there is a point hitting 100 (million) on the y-axis. That means that100 million portable media players were sold in 2008.

Using this same method, we can see that160 million portable media players were sold in 2011. That means that the fraction of portable media players sold in 2008 versus 2011 is 100,000,000 / 160,000,000, which simplifies to5/8.

## Two-Way Tables

Two-way tables efficiently display the distribution of a set of data, organized by the data’s defining characteristics.

These tables often appear throughout both SAT math sections. They are often combined with other concepts like probability, rates, and proportions.

While specific questions might vary, their purpose is the same: the SAT wants to make sure that students know how to read tables correctly!

When analyzing a two-way table on the SAT, pay attention to the following:

- The
**titles of the column(s)** - The
**titles of the row(s)** - Rows or columns that specify
**total values**

Let’s look at an example of an SAT two-way table now.

**How to solve:**

In this problem, the columns reflect the ages of contestants and the rows reflect the genders. To find a specific age/gender combination, simply look at where the two desired variables intersect.

Remember that probability is calculated by dividing the total number of desired outcomes by the total number of possible outcomes.

Here, the desired outcome is either a female under age 40, or a male older than age 40. If we start by looking in the row labeled “female” and then move over to the column labeled “under 40,” we see that 8 people fall into this category.

Using the same process, we can also see that there are 2 males age 40 or older. That means that the total number of subjects in our “desired outcomes” bucket is 8 + 2, or 10.

To find the probability that one of these outcomes will occur, we need to divide by the total number of subjects. To determine the total number of subjects, look in the bottom right corner of the table to find the total number of all gender and age groups. We can see that it’s 25. Therefore, the probability is 10/25, orChoice B.

## Next Steps

The SAT Math sections are very interested in students’ ability to analyze data.

With charts and graphs questions on the math sections, it’s always vital to spend time with the figure or chart *first*. This will minimize the possibility of falling for a trap answer!

Remember that these questions often don’t require intense calculations or knowledge of specific formulas. In fact, they contain all the information you need to find the right answer.

Seeking ways to boost your fluency in data analysis on the SAT? We’ve got you covered. Our expert tutors are here to help you experience confidence on the SAT Math sections and beyond.

Learn more about private SAT tutoring at PrepMaven here!

### Annie

Annie is a graduate of Harvard University (B.A. in English). Originally from Connecticut, Annie now lives in Los Angeles and continues to mentor children across the country via online tutoring and college counseling. Over the last eight years, Annie has worked with hundreds of students to prepare them for all-things college, including SAT prep, ACT prep, application essays, subject tutoring, and general counseling. She is a Master tutor at Princeton Tutoring.

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