PSAT Math Multiple-Choice Question 749: Answer and Explanation

Question: 749

Out of the following options, what is the most unexpected result of the collection of the random sets of numbers?

• A. The values in both sets of data have a range of roughly between 1 and 100.
• B. The selection of 50 random numbers has a significantly higher percentage of values above 50 than does the selection of 20 random numbers.
• C. The selection of 20 random numbers has a much greater range among its values than does the selection of 50 random numbers.
• D. The sets of both data are portrayed as scatter plots rather than as best-fit lines.

Correct Answer: B

Explanation:

(B) Since the values are selected at random, such a high proportion of values greater than 50 in the selection of 50 random numbers is most surprising. With a larger data set, the values would be expected to average closer to the mean than those in the set of 20 random numbers. Since values are taken between 1 and 100, both sets of data should have a range between 1–100, which explains why choice (A) is incorrect. Choice (C) is incorrect because the ranges of the data sets are similar even though the means of the sets are different. Choice (D) is not correct because portraying these random values in a scatter plot is logical. You can impose a best-fit line on top of the scattered data if you would like to determine a trend.