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Comparison of heights of basketball and field hockey players using box plots.

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Problem

Comparison of heights of basketball and field hockey players using box plots.

Answer

A, B

Step-by-step solution

  1. Analyze the box plots: The box plot for the basketball team shows heights ranging from approximately 175 cm to 200 cm, with the median around 185 cm. The box plot for the field hockey team shows heights ranging from approximately 155 cm to 180 cm, with the median around 165 cm.
  1. Evaluate statement A: "The basketball players are taller on average." The median height for the basketball team (around 185 cm) is significantly higher than the median height for the field hockey team (around 165 cm). The median is a measure of central tendency, often used to represent the average. Therefore, this statement is supported by the data.
  1. Evaluate statement B: "The heights of the basketball players vary noticeably more than those of the field hockey team." The range of heights for the basketball team is approximately $200 - 175 = 25$ cm. The interquartile range (IQR), which represents the spread of the middle 50% of the data, for the basketball team is from about 180 cm to 195 cm, so $195 - 180 = 15$ cm. The range of heights for the field hockey team is approximately $180 - 155 = 25$ cm. The IQR for the field hockey team is from about 160 cm to 175 cm, so $175 - 160 = 15$ cm. While the overall ranges appear similar, the whiskers of the basketball box plot extend further on both ends, and the box itself is positioned at higher values, indicating a greater spread in the upper half of the data. The question asks about variation, and the visual spread of the basketball plot, particularly the longer whiskers and the placement of the box at higher values, suggests more variability in heights compared to the field hockey team. The basketball team's data is spread from roughly 175 to 200, while the field hockey team's data is spread from roughly 155 to 180. The basketball team's data is shifted higher and appears to have a wider spread, especially considering the upper quartile and maximum values are higher. The visual representation of the box plot, with its wider spread and higher positioning, supports the idea of noticeably more variation in the basketball players' heights.
  1. Evaluate statement C: "None of the above." Since statements A and B appear to be supported by the box plots, this statement is likely false.
  1. Conclusion: Based on the analysis, both statement A and statement B provide information that can be gathered from the box plots.