Option 2
ANSWER:
The Standard deviation of (7, 9, 10, 11, 13) is 2.
SOLUTION:
Given, data set is (7, 9, 10, 11, 13)
Standard deviation [tex]\sigma=\sqrt{\frac{\Sigma(\mathrm{xi}-\mu) 2}{n}}[/tex]
Where, [tex]\mathrm{x}_{\mathrm{i}}[/tex] is element of data set
[tex]\mu[/tex] is mean of data set
n is total number observations.
Now, mean [tex]\mu=\frac{\text {sum of observations}}{\text {number of observations}}[/tex]
[tex]=\frac{7+9+10+11+13}{5}[/tex]
[tex]=\frac{50}{5}[/tex]
= 10
So, the mean of data set is 10.
Now, standard deviation [tex]\sigma=\sqrt{\frac{(7-10) 2+(9-10) 2+(10-10) 2+(11-10) 2+(13-10) 2}{5}}[/tex]
[tex]\begin{array}{l}{\sigma=\sqrt{\frac{(-3) 2+(-1) 2+(0) 2+(1) 2+(3) 2}{5}}} \\ {\sigma=\sqrt{\frac{9+1+1+9}{5}}} \\ {\sigma=\sqrt{\frac{20}{5}}} \\ {\sigma=2}\end{array}[/tex]
So, the standard deviation is 2.
Hence, the second option is right, i.e. standard deviation is 2.
