PSAT Math Multiple-Choice Question 214: Answer and Explanation

Question: 214

When a drug company wants to introduce a new drug, it must subject the drug to rigorous testing. The final stage of this testing is human clinical trials, in which progressively larger groups of volunteers are given the drug and carefully monitored. One aspect of this monitoring is keeping track of the frequency and severity of side effects. The figure above shows the results for the side effect of headaches for a certain drug. According to the trial guidelines, all moderate and severe headaches are considered to be adverse reactions. Which of the following best describes the data?

• A. The data is symmetric with more than 50 percent of participants having adverse reactions.
• B. The data is skewed to the right with more than 50 percent of participants having adverse reactions.
• C. The data is skewed to the right with more than 75 percent of participants failing to have adverse reactions.
• D. The data is skewed to the right with approximately 50 percent of participants having no reaction at all.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Problem Solving and Data Analysis/Statistics and Probability

Getting to the Answer: Examine the shape of the data and familiarize yourself with the title and the axis labels on the graph. Data is symmetric if it is fairly evenly spread out, and it is skewed if it has a long tail on either side. Notice that the data is skewed to the right, so you can immediately eliminate (A). Choices (B), (C), and (D) all describe the data as skewed to the right, so you'll need to examine those statements more closely. For (B), "adverse reactions" include the last four bars, which represent 89 + 41 + 22 + 8 = 160 participants total, which is not even close to 50 percent of 900, so eliminate (B). Note that you don't need to add all the bar heights to find that there were 900 participants—the title of the graph tells you that. Now look at (C)—"failing to have adverse reactions" means "None" or "Mild" (the first three bars), which represent 900 - 160 = 740 of the 900 participants. Since, 75% of 900 = 675, and 740 is more than 675, (C) is correct. For (D), the "None" column contains 320 participants, which does not equal approximately 50% of 900, so it too is incorrect.