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? 74 70 94 97 29 38 52 59 77 36 37 range = 68 (round to one decimal place as needed.) sample standard deviation = 23.9 (round to one decimal place as needed.) sample variance = 572.4 (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 resulting statistics are meaningless. 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.

Explanation:

Jersey numbers are nominal data (used as labels/identifiers for players, not for numerical measurement like quantity or magnitude). Calculating range, variance, or standard deviation for nominal data is meaningless because these statistics are for interval/ratio data where numbers have numerical meaning. Option A is incorrect as comparing standard deviation and range for nominal data is irrelevant. Options C and D assume jersey numbers have numerical variability meaning, which they don't. So the correct reasoning is that jersey numbers are nominal (replacements for names), making the statistics meaningless.

Answer:

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