SAT TIP: ‘Mean’ Questions on the SAT

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This tip on improving your SAT score was provided by Veritas Prep.

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 to solve these questions in case they come up. While you don’t need to have taken a full course on statistics, you really need to understand three basic concepts: mean, median, and mode. After you learn these definitions, you will need to watch out for how the SAT creates tricky questions based on these concepts. In this article, we will learn more about the arithmetic mean or average and how the SAT might construct a question around this concept.

Mean: The arithmetic mean is the same as what most people call the “average” of a set of numbers. To find the mean, add all of the elements of the set together and divide by the number of elements in the set. So for a set of numbers {6, 7, 9, 10}, the mean is simply (6 + 7 + 9 + 10) / 4 = 8. Questions on the SAT will rarely be this straightforward, though, and will typically require you to go beyond the basic definition. For example:

Robin currently has a mean score of 80 from three tests in her class. What must she score on her fourth and final test to finish the class with a mean score of 82.5?

A. 75
B. 80
C. 85
D. 90
E. 95

For this problem, even if you did not know how to solve it, you should be able to recognize right away that A and B can be eliminated since her final average must be higher than her current average of 80. This can only happen if she scores higher than 80 on the last test. So if you had to guess, you would choose among C, D, and E.

In order to solve this problem, we can apply our knowledge of the mean. To have a mean score of 82.5 over four tests, the sum total of all her test scores needs to be 82.5 x 4 = 330. Currently, across three tests, she has an 80 average, so that total is simply 80 x 3 = 240. As a result, we can see that she needs to get to a total of 330 by scoring 330 – 240 = 90 on her last test. Answer choice D is correct.

You may have noticed already that the SAT rarely asks straightforward questions, such as “What is the average of this set of numbers?” The SAT will take a simple concept like the mean and add some element of critical reasoning to it, such as by giving you the mean and seeing if you can find the original elements in the set. When practicing SAT problems, see if you can come up with ways the SAT might reword the problems to put a more difficult spin on them.

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