Below are the jersey numbers of 11 players randomly selected from a football team. \[ \begin{array}{lllllllllll} 70 & 64 & 42 & 16 & 40 & 14 & 18 & 62 & 98 & 35 & 59 \end{array} \] Range \( =84.0^{\circ} \) (Round to one decimal place as needed.) Sample standard deviation \( =26.3^{*} \) (Round to one decimal place as needed.) Sample variance \( =689.7^{7} \) (Round to one decimal place as needed.) What do the results tell us? A. The sample standard deviation is too large in comparison to the range. B. Jersey numbers are nominal data that are just replacements for names, so the C. Jersey numbers on a football team do not vary as much as expected. D. Jersey numbers on a football team vary much more than expected.
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The range of 84.0 suggests a significant spread between the lowest and highest jersey numbers. However, the sample standard deviation of 26.3 indicates that, despite this range, the majority of the numbers are relatively close to the mean. Since the standard deviation is large compared to some jersey numbers, it suggests that there's substantial variability in players' numbers, leading to the conclusion that jersey numbers on a football team vary much more than expected. While jersey numbers can be seen as nominal data, they also carry meanings related to player positions or roles, influencing how coaches might organize their teams. Thus, even though they replace names, analyzing jersey numbers can provide insights into team composition and strategy.