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The box plots below show the heights (in centimeters) of the players on the Univers...

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Problem

The box plots below show the heights (in centimeters) of the players on the University of Maryland women's basketball and field hockey teams. Which pieces of information can be gathered from these box plots? Choose all answers that apply: A. The basketball players are taller on average. B. The heights of the basketball players vary noticeably more than those of the field hockey team. C. None of the above

Answer

A and B

Step-by-step solution

  1. Analyze the box plots: The box plot for the basketball team is purple, and the box plot for the field hockey team is blue. The horizontal axis represents height in centimeters.
  1. Interpret the box plots: A box plot displays the five-number summary of a dataset: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box itself represents the interquartile range (IQR), which contains the middle 50% of the data. The line inside the box is the median.
  1. Evaluate option A: "The basketball players are taller on average." The median height for the basketball team appears to be around 185 cm, while the median height for the field hockey team is around 165 cm. Since the median is a measure of central tendency (often used as a proxy for the average when distributions are not heavily skewed), the basketball players are indeed taller on average.
  1. Evaluate option B: "The heights of the basketball players vary noticeably more than those of the field hockey team." To assess variation, we can look at the range (maximum - minimum) or the interquartile range (IQR = Q3 - Q1). For the basketball team, the IQR is approximately from 175 cm to 195 cm, so the IQR is about 20 cm. The total range is from about 150 cm to 200 cm, a range of 50 cm. For the field hockey team, the IQR is approximately from 160 cm to 170 cm, so the IQR is about 10 cm. The total range is from about 155 cm to 180 cm, a range of 25 cm. Since both the IQR and the total range are larger for the basketball team, their heights vary noticeably more than those of the field hockey team.
  1. Conclusion: Both statements A and B can be gathered from the box plots.