SAT Math Multiple Choice Question 525: Answer and Explanation

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Test Information

Question: 525

15. The figure shows the age distribution of homebuyers and the percent of the market each age range makes up in a particular geographic region.

Based on the information in the figure, which of the following statements is true?

  • A. The shape of the data is skewed to the right, so the mean age of homebuyers is greater than the median.
  • B. The shape of the data is skewed to the left, so the median age of homebuyers is greater than the mean.
  • C. The shape of the data is fairly symmetric, so the mean age of homebuyers is approximately equal to the median.
  • D. The data has no clear shape, so it is impossible to make a reliable statement comparing the mean and the median.

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Problem Solving and Data Analysis / Statistics and Probability

Strategic Advice: Some data sets have a head, where many data points are clustered in one area, and one or two tails, where the number of data points slowly decreases to 0. Examining the tail will help you describe the shape of the data set. A data set is skewed in the direction of its longest tail.

Getting to the Answer: The graph in this question has its tail on the right side, so the data is skewed to the right. When data is skewed to the right, the mean is greater than the median because the mean is more sensitive to the higher data values in the tail than is the median, so (A) is correct. If you're not sure about the mean/median part, read the rest of the answer choices—none of them describes the data as skewed to the right, so you can eliminate all of them.

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