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SAT Tip: Statistics 'à la Mode'

SAT Tip: Statistics 'à la Mode'

Photograph by Floriano Rescigno/Getty Images


Statistics questions are rare on the SAT, but they do appear a handful of times on any given test. As a result, students looking to score a perfect 2400 need to know at least some basics of statistics in order to solve these questions in case they come up. While you don’t need to be a statistician, to do well you really need to understand three basic concepts for the SAT: mean, median, and mode. After you learn these definitions, you will need to watch out for how the SAT creates tricky questions around these concepts. In this article, we will learn more about the mode, or the most commonly occurring element in a set, and how the SAT could turn a seemingly simple concept into a problem-solving adventure.

Mode – The mode of a set of numbers is simply the most commonly occurring elements in the set. For the set {3,4,5,5,7,9}, the mode is 5, since 5 occurs the most often. Note that a set can have multiple modes if there is a tie for the most times a number appears. So for the set {3,3,5,6,10,10,11}, there are two modes, 3 and 10, since they both appear the most (2 times). Questions on the SAT will often combine knowing the mode with other math concepts.

Consider the following free-response question.

{x, 2x, 2x, y, 6, y – 2, 12, 13}

If the only mode of the set above is 4 and y = 6, what is the value of x?

You see how the SAT can make a simple concept confusing? To solve this problem, let’s work with what we know and do the first step. We know that y = 6, so let’s replace that in the set and we have:
{x, 2x, 2x, 6, 6, 4, 12, 13)

Now, since we know that the mode of the set is 4, 4 must appear the most in the set. This can only be true if the two 2x terms are equal to 4 since that would give us a set of {x, 4, 4, 6, 6, 4, 12, 13}. Thus, if 2x = 4, then x = 2 and our set looks like {2, 4, 4, 4, 6, 6, 12, 13}. You can then grid in “2” for this free-response question.

As you can see, questions on the SAT involving the mode will not simply test your ability to identify the mode, but will extend the concept with other elements that require you to combine your knowledge of the mode with higher-level reasoning. In the question above, we had to know what the mode meant and also reason our way to the conclusion that for the mode to be 4, x must be equal to 2. Much of the difficulty of SAT math does not come from the math concepts themselves, but in how the SAT incorporates critical reasoning into the questions.

Plan on taking the SAT soon? Sign up for a trial of Veritas Prep SAT 2400 on Demand!

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