Respuesta :
For this type of problem we use the following formula:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{\sum^{}_{}(x_i-\mu)^2}{N},} \\ \\ \end{gathered}[/tex]where μ is the population mean, xi is each value from the population, and N is the size of the population.
First, we compute the population mean in order to do that we use the following formula:
[tex]\mu=\frac{\Sigma x_i}{N}\text{.}[/tex]Substituting each value of x_i in the above formula we get:
[tex]\mu=\frac{6+8+9+6+5}{5}=\frac{34}{5}=6.8.[/tex]Now, we compute the difference of each x_i with the mean:
[tex]\begin{gathered} 6-6.8=-0.8, \\ 8-6.8=1.2, \\ 9-6.8=2.2, \\ 6-6.8=-0.8, \\ 5-6.8=-1.8. \end{gathered}[/tex]Squaring each result we get:
[tex]\begin{gathered} (-0.8)^2=0.64, \\ (1.2)^2=1.44, \\ (2.2)^2=4.84, \\ (-0.8)^2=0.64, \\ (-1.8)^2=3.24. \end{gathered}[/tex]Now, we add the above results:
[tex]0.64+1.44+4.84+0.64+3.24=10.8.[/tex]Dividing by N=5 we get:
[tex]\frac{10.8}{5}=2.16.[/tex]Finally, taking the square root of 2.16 we obtain the standard deviation,
[tex]\sigma=\sqrt[]{2.16}\approx1.47.[/tex]Answer:
[tex]\sigma=1.47.[/tex]