The range of the given data is 13, the population mean of the given data set is 8.6, the population variance of the given data set is 15.85, and the population standard deviation of the given data set is 3.98 and this can be determined by using the given data.
Given :
The numbers of regular season wins for 10 football teams in a given season are given below.
2,9, 15, 5, 14, 8, 11, 7, 4, 10
a) The range of the given data is:
[tex]\rm Range = 15 - 2[/tex]
[tex]=13[/tex]
b) The population mean of the given data set is:
[tex]\rm Mean =\dfrac{2+9+15+5+14+8+11+7+4+10}{10}[/tex]
[tex]\rm Mean = \dfrac{85}{10} = 8.5[/tex]
Mean = 8.6 (round off to the nearest tenth)
c) The population variance of the given data set is:
[tex]\sigma^2 = \dfrac{1}{10}\times[(2-8.5)^2+(9-8.5)^2+(15-8.5)^2+(5-8.5)^2+(14-8.5)^2+(8-8.5)^2+(11-8.5)^2+(7-8.5)^2+(4-8.5)^2+(10-8.5)^2}][/tex]
[tex]\sigma^2= 15.85[/tex]
d) The population standard deviation of the given data set is:
[tex]\sigma =\sqrt{15.85} = 3.981[/tex]
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https://brainly.com/question/13905583
