Data in the SAT

As we pass through October, many high schoolers have already started to prepare for what is arguably the most important standardized test in high school––the SAT.

One data-related question that the SAT loves to bring up is about the box plot, a simple chart that depicts useful features of a data set like the median, interquartile region, and range. A simple box plot looks like the image below:

Today, I will be clarifying how to recognize these features on the box plot chart to help with potential SAT questions. Let's start by breaking down the parts of the graph.

The line that runs along the number line with dots at the end represents the entire span of the data, where the left end is the lowest value in the set and the right end is the highest. You can find the range by simply subtracting the lowest value from the highest value.

One of the nicest quirks of the box plot is the ease with which you can recognize the quartiles, which represents the overall distribution of the data in fourths. The region from the left end of the data to where the first box starts represents the lower 25% of the data. The beginning of the first box to the end of the second box is the interquartile range and represents the middle 50% of the data. From the end of the second box to the right end represents the top 25%.

The median, the middle value when all points of the data are lined up in order, is simply the line splitting the two boxes.

It's important to note that most box plots don't look as clean and symmetrical as the first example. For example, consider the diagram below.

In these examples, the data is slightly right–skewed.

Though the box plot seems simple enough, its structure can be a bit misleading. It's important to remember, especially for the SAT, that:

1. Each sector of the plot represents 25% of the data, no matter how long one side of the box or the line segment is.

2. A box plot does not tell us how many values are in the data set

3. A box plot does not tell us anything about the mean or mode

4. Box plots are more about how data is spread, not what it actually is

With this information, try answering the following practice SAT question from CollegeBoard's question bank:

The correct answer is...

Option C! The box plot tells us nothing about the mean, so we can automatically eliminate options A and B. We know the median is the line splitting the two boxes. In group 1, the median is 25. In group 2, the median is 24. Therefore, we know that the median mass of group 1 is greater than that of group 2. Option C is correct.

Credit:

Khan Academy. “Box Plot Review,” Khan Academy, 2010.

Taylor, Courtney. “An Introduction to the Interquartile Range,” ThoughtCo, 8 May 2025.