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One-variable data: Distributions and measures of center and spread SAT question

Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.

Data set A consists of 9 data values, each of which is the integer 5.
Data set B consists of 10 data values, nine of which are the integer 5, and one of which is the integer 100.

Which of the following statements about the means and medians of data set A and data set B is true?

ExplanationShow

Choice A is correct. The mean of a data set is the sum of the values divided by the number of values. The mean of data set A is the fraction 45 over 9, or 5. The mean of data set B is the fraction 145 over 10, or 14.5. Thus, the means are different. The median of a data set is the middle value when the values are ordered from least to greatest. The medians of data sets A and B are both 5. Therefore, the medians are the same, so only the means are different.

Choices B, C, and D are incorrect and may result from conceptual or calculation errors.

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