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:

Thus, the range of the data is 9.0.
(B)
The formula to compute the population variance is:

Compute the mean of the data set:

Compute the variance as follows:
![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](https://tex.z-dn.net/?f=Var%3D%5Cfrac%7B1%7D%7Bn%7D%20%5Csum%20%28x_%7Bi%7D-%5Cbar%20x%29%5E%7B2%7D%5C%5C%3D%5Cfrac%7B1%7D%7B10%7D%5B%282-6.5%29%5E%7B2%7D%2B%283-6.5%29%5E%7B2%7D%20%2B%284-6.5%29%5E%7B2%7D%2B...%2811-6.5%29%5E%7B2%7D%5D%5C%5C%3D8.25)
Thus, the population variance is 8.25.
(C)
The population standard deviation is:

Compute the population standard deviation of the data set:

Thus, the population standard deviation is 2.87.