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?
51 26 29 23 55 39 63 79 16 65 53
sample standard deviation = 20.2 (round to one decimal place as needed.)
sample variance = 408.0 (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. jersey numbers on a football team do not vary as much as expected.
c. jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
d. the sample standard deviation is too large in comparison to the range.

Explanation:

Step1: Calculate the range

The range is the difference between the maximum and minimum values.
Maximum value \(= 79\), minimum value \(= 16\)
\(Range=79 - 16\)
\(Range = 63\)

Step2: Analyze the nature of jersey numbers

Jersey numbers are used to identify players (like a name - tag). They do not have a numerical order in the sense of magnitude for arithmetic operations (e.g., \(29\) as a jersey number does not mean \(29\) units of something in a meaningful numerical way for variance/standard - deviation calculations related to quantity).

Answer:

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