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?

 14 65 76 16 7 35 92 48 22 83 98 

Range = (Round to one decimal place as needed.) 

Sample standard deviation = (Round to one decimal place as needed.) 

Sample variance (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.

Answer 1

Range=Maximum Value–Minimum Value

=98-7

=91

Mean=(14+65+76+16+7+35+92+48+22+83+98)/11

=556/11

=50.55

x	(x-Mean)	(x-Mean)^2
14	-36.55	1335.9
65	14.45	208.8
76	25.45	647.7
16	-34.55	1193.7
7	-43.55	1896.6
35	-15.55	241.8
92	41.45	1718.8
48	-2.55	6.5
22	-28.55	815.1
83	32.45	1053
98	47.45	2251.5

Total

11369.4

Sample standard deviation=√{(x-mean)^2}/(n-1)

=√11369.4/(11-1)

=√11369.4/10

=33.7

Sample variance=(√11369.4/(11-1))^2

=(√11369.4/10)^2

=11369.4/10

=1136.94

=1136.9

The results tell us option(d) which states that Jersey numbers are just nominal data which are just replacement for names so the resulting statistics are meaningless. It is because the players choose their jersey numbers as their own wish and their is no quantitative data to it in most cases.

Option (a) is not right because jersey numbers can vary much.

Option (b) is not right because the sample standard deviation is not too large as compared to range.

Option (c) is not right because can vary between teams and nothing can be expected by how much they vary.