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

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

  • From left to right the values of the vertical bars in the Group 1 box plot are as follows:
    • First vertical bar: 21
    • Second vertical bar: 22
    • Third vertical bar: 25
    • Fourth vertical bar: 26
    • Fifth vertical bar: 28
  • From left to right the values of the vertical bars in the Group 2 box plot are as follows:
    • First vertical bar: 22
    • Second vertical bar: 23
    • Third vertical bar: 24
    • Fourth vertical bar: 25
    • Fifth vertical bar: 28

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?

ExplanationShow

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 is kilograms, and the median mass of the gazelles in group is kilograms. Since kilograms is greater than kilograms, the median mass of group is greater than the median mass of group .

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.

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