This page is part of my unofficial solutions manual to the GRE Paper Practice Book (2e), a free resource available on the ETS website. They publish the questions; I explain the answers. If you haven’t worked through the Practice Book, give Section 6 a shot before reading this!

6.20: State Populations, Pt. 4

Rounding out this block is a basic descriptive-statistics question. In order to find the median of a data set, we have to arrange the elements of that set in increasing order. We can’t quite do that here, because we don’t know the values of the individual elements. But that’s fine, because we don’t need to determine the median precisely. We just need to know its approximate whereabouts.

Regardless of their order within the category, the 15 least populous states will all be in category A. (In other words, if we could actually arrange the states in order of increasing population, the first 15 entries in the list would all be from category A.) The next least populous category is B, which contains 9 states. Taking these two categories together gives us 24 out of our 50 states, which is still not enough to get us to the halfway point of the list. The next 12 entries in the list (states #25 through #36 in order of increasing population) belong to category C.

Potential plot twist: when a data set has an even number of elements, there are two “middle numbers” and the median is the average of those. So the median here would be the average population of the 25th and 26th states in our list. But both of those states lie in category C, so our median must also be in category C. Conveniently, this time the category letters line up with the answer choices, so the correct answer is (C).

Math Review Reference

For more on this topic, see the following sections of the GRE Math Review:

• 4.1: Graphical Methods for Describing Data (pp. 62-64)
• 4.2: Numerical Methods for Describing Data (pp. 68-69)