Answer:
A. 6.5
Step-by-step explanation:
First we find the average [tex]\bar{x}[/tex] of the 9 data:
[tex]\bar{x} =\frac{\sum_{x=1}^{n}x_{i}}{n}[/tex]
Where n is the data number, that in this case is 9.
[tex]\bar{x} =\frac{1+ 2+ 11+ 8+ 16+ 16+20+ 16+ 18}{9}=12\\[/tex]
The formula of the standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=\sqrt{\frac{\sum_{x=1}^{n}(x_{i}-\bar{x})^{2}}{n}}[/tex]
We replace the data and find the value of the standard deviation:
[tex]\sigma=\sqrt{\frac{(1-12)^{2}+(2-12)^{2}+(11-12)^{2}+(8-12)^{2}+(16-12)^{2}+(16-12)^{2}+(20-12)^{2}+(16-12)^{2}+(18-12)^{2}}{9}}[/tex]
[tex]\sigma=\sqrt{\frac{(-11)^{2}+(-10)^{2}+(-1)^{2}+(-4)^{2}+(4)^{2}+(4)^{2}+(8)^{2}+(4)^{2}+(6)^{2}}{9}}=6,54[/tex]
We approximate the number and the solution is 6,5
