The formula to calculate the standard deviation is:
[tex]s=\sqrt[]{\frac{\sum ^n_{i\mathop=1}(x_i-\bar{x})^2}{n-1}}[/tex]
first, calculate the mean of the data sample
[tex]\begin{gathered} \bar{x}=\frac{19.83+20.14+19.28+19.75+19.39+19.86+19.02+19.71}{8} \\ \bar{x}=19.6225 \end{gathered}[/tex]
then, apply the standard deviation formula
[tex]\begin{gathered} s=\sqrt[]{\frac{(19.83-19.6225)^2+(20.14-19.6225)^2+(19.28-19.6225)^2+(19.75-19.6225)^2+(19.39-19.6225)^2+(19.86-19.6225)^2+(19.02-19.6225)^2+(19.71-19.6225)^2}{7}} \\ \end{gathered}[/tex][tex]s\approx0.36262[/tex]
