The problem presents two box plots showing the height distributions of basketball and field hockey players. We are asked to determine which of the given statements can be inferred from these box plots.
Probability and StatisticsBox PlotsData AnalysisDescriptive StatisticsMedianRangeInterquartile Range
2025/3/10
1. Problem Description
The problem presents two box plots showing the height distributions of basketball and field hockey players. We are asked to determine which of the given statements can be inferred from these box plots.
2. Solution Steps
The box plot provides information about the median, quartiles, and range of the data.
Statement A: "The basketball players are taller on average." The median of the basketball team's heights is approximately 180 cm, while the median of the field hockey team's heights is approximately 165 cm. Since the median represents the "average" height, it seems reasonable to conclude that basketball players are taller on average. Thus, statement A is likely true.
Statement B: "The heights of the basketball players vary noticeably more than those of the field hockey team." The range of the basketball team's heights is approximately from 145 cm to 205 cm, which is a range of 60 cm. The range of the field hockey team's heights is approximately from 158 cm to 180 cm, which is a range of 22 cm. The interquartile range (IQR) for the basketball team is approximately from 170 cm to 195 cm, which is 25 cm. The IQR for the field hockey team is approximately from 160 cm to 170 cm, which is 10 cm. Since both the range and IQR are larger for the basketball team, the heights of the basketball players vary noticeably more than those of the field hockey team. Thus, statement B is also likely true.
3. Final Answer
A, B