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?

23 53 67 61 66 91 27 85 98 44 73
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Part 1
Range= enter your response here ​(Round to one decimal place as​ needed.)
Part 2
Sample standard deviation= enter your response here ​(Round to one decimal place as​ needed.)
Part 3
Sample variance= enter your response here ​(Round to one decimal place as​ needed.)
Part 4
What do the results tell​ us?
A.
Jersey numbers are nominal data that are just replacements for​ names, so the resulting statistics are meaningless.
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 on a football team vary much more than expected.

Answer 1

Part 1:

Range = 98 - 23 = 75

Part 2:

First, find the sample mean:

Mean = (23 + 53 + 67 + 61 + 66 + 91 + 27 + 85 + 98 + 44 + 73)/11 = 61.9

Then, find the sum of the squared differences between each jersey number and the mean:

(23-61.9)^2 + (53-61.9)^2 + (67-61.9)^2 + (61-61.9)^2 + (66-61.9)^2 + (91-61.9)^2 + (27-61.9)^2 + (85-61.9)^2 + (98-61.9)^2 + (44-61.9)^2 + (73-61.9)^2 = 12388.4

Sample variance = 12388.4/10 = 1238.84

Sample standard deviation = √1238.84 = 35.17

Part 3:

Sample variance = 1238.84

Part 4:

The results tell us that there is a relatively large range in jersey numbers, with a difference of 75 between the highest and lowest numbers. The sample variance and standard deviation also indicate that there is a considerable amount of variability in the data, with jersey numbers varying significantly from the mean. This suggests that there is no pattern or structure to the jersey numbers on the football team, and that they are assigned somewhat randomly.

Explanation: