SAT Tip: Statistics and the Median

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

Questions about statistics 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 when they do come up. While you don’t need to have taken AP statistics, you really need to understand three basic concepts to do well on 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 median, or middle number in a set, and how the SAT might turn this simple concept into a tougher question on the test.

Median: The median of a set of numbers is simply the middle value if you arranged the numbers in order of increasing value. If no perfect “middle” number exists, as in the case of sets with an even number of elements, the median is the average of the two middle numbers. For example, the median of the set {3, 3, 5, 7, 8} would be 5, since 5 is the middle number; the median of the set {3, 3, 5, 7, 8, 10} would be 6, since the middle two numbers are 5 and 7, and the average of those numbers is 6.

Questions on the SAT that involve the median will typically test whether you can apply your knowledge of the definition of the median. Consider the following question:
Consider a set of 5 positive integers. Which of the following will NOT affect the value of the median of this set of numbers?

I.     Multiplying each number by 2
II.    Subtracting 1 from the smallest number
III.   Subtracting 1 from the largest number

A.      I only
B.      II only
C.      III only
D.      I and II
E.      II and III

To test these cases, it’s usually best to come up with a set of numbers and try to reason it out. Let’s use the set {2,4,5,7,10}. Its median is currently 5.

If we multiple each number by 2, we have {4,7,10,14,20}. The median is now 10, so it has changed. So we can cross off answer choices A and D.

If we subtract 1 from the smallest number, we have {1,4,5,7,10}. The median is still 5, so numeral II is correct, and we are left with answer choices B and E.

If we subtract 1 from the largest number, the set becomes {2,4,5,7,9}. The median has not changed here, either, so III checks out, and we can select answer choice E as our answer.

Bonus: Consider how your answer to this question might change if the restriction to a set of 5 positive integers were changed to “a set of 2 or more integers.”

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