SOLUTION
The given data set is
[tex]19,15,22,16,23,19[/tex]The mean of the data is
[tex]\begin{gathered} \bar{x}=\frac{19+15+22+16+23+19}{6} \\ \bar{x}=\frac{114}{6} \\ \bar{x}=19 \end{gathered}[/tex]The standard deviation is calculated using
[tex]\sigma=\sqrt{\frac{1}{N}\sum(x-\bar{x})^2}[/tex]Substituting the data gives
[tex]\begin{gathered} \sigma=\sqrt{\frac{(19-19)^2+(15-19)^2+(22-19)^2+(16-19)^2+(23-19)^2+(19-19)^2}{6}} \\ \sigma=8.333 \end{gathered}[/tex]Therefore the standard deviation is 8.333
