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Problem-Solving and Data Analysis / One-variable data: Distributions and measures of center and spread Difficulty: Medium

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

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

Only the means are different.

Only the medians are different.

Both the means and the medians are different.

Neither the means nor the medians are different.

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Explanation

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.