PSAT Math Multiple-Choice Question 223: Answer and Explanation

Question: 223

The United States Constitution requires that any candidate for the presidency be at least 35 years of age, although no president to date has been that young. The figure above shows the distribution of the ages of the presidents through 2012 at the time they were inaugurated. Based on the information shown, which of the following statements is true?

• A. The shape of the data is skewed to the left, so the mean age of the presidents is greater than the median.
• B. The shape of the data is fairly symmetric, so the mean age of the presidents is approximately equal to the median.
• C. The data has no clear shape, so it is impossible to make a reliable statement comparing the mean and the median.
• D. The same number of 55-or-older presidents have been inaugurated as ones who were younger than 55, so the mean age is exactly 55.

Correct Answer: B

Explanation:

B

Difficulty: Easy

Category: Problem Solving and Data Analysis/Statistics and Probability

Getting to the Answer: Quickly read each answer choice. Cross out false statements as you go. Stop when you arrive at a true statement. There is no long "tail" of data on either side, so the shape is not skewed and you can eliminate (A). The shape of the data is symmetric because the data is fairly evenly spread out, with about half of the ages above and half below the median. When the shape of a data set is symmetric, the mean is approximately equal to the median, so (B) is correct. Don't let (D) fool you—the median is 55, not the mean.