Answer: Option a
[tex]\sigma=2.83[/tex]
Step-by-step explanation:
The formula for calculating the standard sigma deviation is:
[tex]\sigma=\sqrt{\frac{\sum_{i=1}^n(X_i-{\displaystyle {\overline {x}}})^2}{N}}[/tex]
Where
[tex]{\displaystyle {\overline {x}}}[/tex] is the average
[tex]X_1, X_2, ..., X_i[/tex] is the data set
N is the amount of data
First we calculate the average
[tex]{\displaystyle {\overline {x}}}=\frac{2+4+6+8+10}{5}[/tex]
[tex]{\displaystyle {\overline {x}}}=6[/tex]
Now we calculate the square differences
[tex](2-6)^2=16\\\\(4-6)^2=4\\\\(6-6)^2=0\\\\(8-6)^2=4\\\\(10-6)^2=16[/tex]
Then
[tex]\sum(X_i-{\displaystyle {\overline {x}}})^2} = 16+ 4+0+4+16=40[/tex]
Finally the standard deviation for the set of data is:
[tex]\sigma=\sqrt{\frac{40}{5}}[/tex]
[tex]\sigma=2.83[/tex]
