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

The box plots summarize the masses, in kilograms, of two groups of gazelles. Based on the box plots, which of the following statements must be true?

The mean mass of group 1 is greater than the mean mass of group 2.

The mean mass of group 1 is less than the mean mass of group 2.

The median mass of group 1 is greater than the median mass of group 2.

The median mass of group 1 is less than the median mass of group 2.

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Explanation

Choice C is correct. The median of a data set represented in a box plot is represented by the vertical line within the box. It follows that the median mass of the gazelles in group $1$ is $25$ kilograms, and the median mass of the gazelles in group $2$ is $24$ kilograms. Since $25$ kilograms is greater than $24$ kilograms, the median mass of group $1$ is greater than the median mass of group $2$ .

Choice A is incorrect. The mean mass of each of the two groups cannot be determined from the box plots.

Choice B is incorrect. The mean mass of each of the two groups cannot be determined from the box plots.

Choice D is incorrect and may result from conceptual or calculation errors.