To answer this question we need to remember the definition of the variance:
[tex]s^2=\frac{1}{n-1}\sum_{i\mathop{=}1}^n(x-\bar{x})^2[/tex]
To helps us calculate it we have the table shown below:
From it we can calculate the mean:
[tex]\bar{x}=\frac{541}{11}=49.181818[/tex]
Now, we have (on the table) the values x minus the mean and then the square of this. Adding we have:
[tex]\sum_{i\mathop{=}1}^n(x-\bar{x})^2=7719.6364[/tex]
And hence the variance is:
[tex]s^2=\frac{7719.6364}{11-1}=771.96364[/tex]
The standard deviation is the square root of the variance, then we have:
[tex]\begin{gathered} s=\sqrt{771.96364} \\ s=27.784234 \end{gathered}[/tex]
Finally the range is the maximum value minus the minimum, then:
[tex]range=81-1=80[/tex]
Therefore:
Range 80
Standard deviation 27.8
Variance 772
Now, jersey numbers don't represent any relation between the numbers they have which means that they are nominal data and therefore the last correct option is A.
