The problem presents two box plots, one for the heights of basketball players and one for the heights of field hockey players. The task is to determine which statements can be gathered from these box plots regarding the heights of the players.
Probability and StatisticsBox PlotsData AnalysisStatistical ComparisonMedianInterquartile RangeRange
2025/3/10
1. Problem Description
The problem presents two box plots, one for the heights of basketball players and one for the heights of field hockey players. The task is to determine which statements can be gathered from these box plots regarding the heights of the players.
2. Solution Steps
The box plot for the basketball team is to the right of the box plot for the field hockey team.
The median of basketball team appears to be around 185 cm, and the median of the field hockey team appears to be around 165 cm. The median of the basketball players is taller.
Also, the length of the basketball team's boxplot is longer than the length of the field hockey team's boxplot.
Option A: "The basketball players are taller on average." Since the median height of the basketball players is greater than the median height of the field hockey players, this statement is supported by the box plots.
Option B: "The heights of the basketball players vary noticeably more than those of the field hockey team." The range of the basketball players' heights (difference between the maximum and minimum) is greater than the range of the field hockey players' heights. The interquartile range (length of the box) is also longer for the basketball team than the field hockey team. Thus, this statement is also true.
3. Final Answer
A and B