you will have to use the variance formula
[tex]s^2=\frac{\sum ^{\infty}_{n\mathop=0}(x_i-\bar{x})^2}{n-1}[/tex]where n is the number of data that was given
start by calculating the average
[tex]\begin{gathered} \bar{x}=\frac{8+13+15+17+22}{5} \\ \bar{x}=15 \end{gathered}[/tex]replace on the formula
[tex]\begin{gathered} s^2=\frac{(8-15)^2+(13-15)^2+(15-15)^2+(17-15)^2+(22-15)^2}{4} \\ s^2=\frac{106}{4} \\ s^2=26.5 \end{gathered}[/tex]the variance will be 26.5
to calculate the standard deviation you do the square root of the variance
[tex]\begin{gathered} s=\sqrt[]{26.5} \\ s\approx5.148 \end{gathered}[/tex]