Respuesta :
We need to use the variance and standard deviation for a sample:
The equation for a variance is:
[tex]s^2=\frac{\Sigma(x-x^-)^2}{n-1}[/tex]Where x⁻ is the mean of x and n is the total number of values.
First, let us find the mean:
[tex]Mean=\frac{38+45+27+42+17+36+10+21+33+36}{10}[/tex]Then :
[tex]mean=30.5[/tex]Now, we can find the variance:
[tex]s^2=\frac{\Sigma x-30.5}{10-1}=\frac{(38-30.5)+(45-30.5)+(27-30.5)+(42-30.5)+(17-30.5)+(36-30.5)+(10-30.5)+(21-30.5)+(33-30.5)+(36-30.5)}{9}[/tex]Simplify it:
[tex]s^2=130.0555[/tex]Now, we need to use the next formula to find the standard deviation:
[tex]s=\sqrt{\frac{\Sigma(x-x^-)^2}{n-1}}[/tex]Then:
[tex]s=\sqrt{\frac{(38-30.5)^2+(45-30.5))^2+(27-30.5))^2+(42-30.5))^2+(17-30.5))^2+(36-30.5))^2+(10-30.5))^2+(21-30.5))^2+(33-30.5))^2+(36-30.5))^2}{9}}[/tex]Then, the standard deviation is:
[tex]s=11.40419[/tex]