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Problem-Solving and Data Analysis Difficulty: Easy

Data set A is the set consisting of the following seven numbers: 1 comma 2, comma 3, comma 4, comma 5, comma 6, comma 7. Data set B is the set consisting of the following seven numbers: 1 comma 1, comma 2, comma 2, comma 3, comma 3, comma 4.

Which of the following statements correctly compares the means of data set A and data set B?

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Explanation

Choice D is correct. The mean of a data set is found by dividing the sum of the values in the data set by the number of values in the data set. Therefore, the mean of data set A is the fraction with numerator 1 plus 2, plus 3, plus 4, plus 5, plus 6, plus 7, and denominator 7, equals, the fraction 28 over 7, or 4. The mean of data set B is the fraction with numerator 1 plus 1, plus 2, plus 2, plus 3, plus 3, plus 4, and denominator 7, equals, the fraction 16 over 7, or approximately 2.2857. Therefore, the mean of data set A is greater than the mean of data set B.

Alternate approach: Data set A and data set B are both ordered from least to greatest value. Besides the first value in each data set, which is 1, each value in ordered data set B is less than the respective value in ordered data set A. Therefore, conceptually, the mean of data set A must be greater than the mean of data set B.

Choices A, B, and C are incorrect and may result from various misconceptions or miscalculations.