SAT Math Multiple Choice Question 865: Answer and Explanation

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Question: 865

10. A study of gasoline prices across a particular state showed that the state's meangas price was $2.87 per gallon, and the median gas price was $3.25 per gallon. Whichof the following most likely accounts for the difference between the mean and mediangas prices in this state?

  • A. A few areas of the state had substantially lower gas prices than the rest.
  • B. A few areas of the state had substantially higher gas prices than the rest.
  • C. The majority of areas in the study had gas prices between $2.87 and $3.25 per gallon.
  • D. An error was made during data collection or data analysis.

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Strategic Advice: Knowing when the mean and median of a data set are equal is the key to answering a question like this.

Getting to the Answer: The mean of a data set is approximately equal to the median when the data has a symmetrical distribution. In this scenario, the mean and median are not equal, which indicates that the data distribution is asymmetric. The difference between them is fairly large (compared to the values themselves), which could be explained by the presence of outliers (values that are significantly smaller or larger than the other values in the data). Outliers affect the mean of a data set but not the median. Because the mean is lower than the median, the outliers must also be on the low side, which means you can reasonably conclude that a few areas in the study had gas prices that were much lower than those elsewhere in the state. Choice (A) is correct.

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