SAT Math Multiple Choice Question 456: Answer and Explanation

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Question: 456

6.

The bar graph shows median household incomes in a certain geographic region according to the age of the highest earner in the household. When presenting the data, the researcher decides to exclude the first age bracket (15-24), because it includes minors, which will likely skew the results because most minors do not have full-time jobs. The researcher also decides to exclude the last age bracket (65+) because it includes retirees, which is again likely to skew the results for the same reason. Which of the following statements most likely describes how this will affect the data overall?

  • A. It will significantly change the median, but not the mean.
  • B. It will significantly change the mean, but not the median.
  • C. It will significantly change both the mean and the median.
  • D. There will be no significant change to either the mean or the median.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Strategic Advice: The mean is the average of the data, while the median is the midpoint. When the shape of the data is symmetric, the mean is approximately equal to the median.

Getting to the Answer: The two age brackets that are being removed contain the same amount of data and are on opposite sides of the center of the data, so there will be no significant change to either the mean or the median.

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