Question

below are the jersey numbers of 11 players randomly selected from a football team. find the range, variance, and standard deviation for the given sample data. what do the results tell us?
85 42 11 2 61 12 46 10 47 29 8
range = 83 (round to one decimal place as needed)
sample standard deviation = 26.7 (round to one decimal place as needed)
sample variance = 697.0 (round to one decimal place as needed)
what do the results tell us?
a. jersey numbers on a football team vary much more than expected
b. the sample standard deviation is too large in comparison to the range
c. jersey numbers on a football team do not vary as much as expected
d. jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Explanation:

Step1: Analyze the nature of jersey numbers

Jersey numbers are used to identify players. They do not have a numerical value in the sense of magnitude for calculations like range, variance, and standard deviation. They are nominal data (used for naming or labeling).

Step2: Evaluate each option

• Option A: Jersey numbers are not for showing variation in a meaningful numerical way.
• Option B: The comparison between standard deviation and range is not relevant as the data is nominal.
• Option C: The concept of expected variation for nominal data (jersey numbers) in a numerical sense is not applicable.
• Option D: Since jersey numbers are nominal data (just for identification like names), calculating range, variance, and standard deviation is meaningless.

Answer:

D. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.