Respuesta :
Answer:
The range of the data is 9.0.
The population variance is 8.25.
The population standard deviation is 2.87.
Step-by-step explanation:
The data set is: S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
(A)
The range of a data set is the difference between the maximum and minimum value of the data set.
Compute range as follows:
[tex]Range=Max.-Min.=11-2=9[/tex]
Thus, the range of the data is 9.0.
(B)
The formula to compute the population variance is:
[tex]Var=\frac{1}{n} \sum (x_{i}-\bar x)^{2}[/tex]
Compute the mean of the data set:
[tex]\bar x=\frac{1}{n} \sum x_{i}\\=\frac{1}{10}(2+3+4+5+6+7+8+9+10+11)\\=6.5[/tex]
Compute the variance as follows:
[tex]Var=\frac{1}{n} \sum (x_{i}-\bar x)^{2}\\=\frac{1}{10}[(2-6.5)^{2}+(3-6.5)^{2} +(4-6.5)^{2}+...(11-6.5)^{2}]\\=8.25[/tex]
Thus, the population variance is 8.25.
(C)
The population standard deviation is:
[tex]SD=\sqrt{Var} = \sqrt{\frac{1}{n} \sum (x_{i}-\bar x)^{2}}[/tex]
Compute the population standard deviation of the data set:
[tex]SD=\sqrt{Var} = \sqrt{8.25}=2.87[/tex]
Thus, the population standard deviation is 2.87.
