The standard deviation for a sample is given by:
[tex]s=\sqrt[]{\frac{\sum^n_{i\mathop=1}(x_i-\bar{x})}{n-1}}[/tex]where n is the sample size, xi are the values of the data and x bar is the mean of the data.
Let's find the mean first:
[tex]\begin{gathered} \bar{x}=\frac{\sum ^n_{i\mathop=1}x_i}{n} \\ \bar{x}=\frac{10.8+15.3+48.6+45.1+21.3+19.9}{6} \\ \bar{x}=\frac{161}{6} \\ \bar{x}=26.83 \end{gathered}[/tex]Now that we have the mean we can calculate the standard deviation:
[tex]\begin{gathered} s=\sqrt[]{\frac{\sum^n_{i\mathop{=}1}(x_i-\bar{x})}{n-1}} \\ =\sqrt[]{\frac{(10.8-26.83)^2+(15.3-26.83)^2+(48.6-26.83)^2+(45.1-26.83)^2+(21.3-26.83)^2+(19.9-26.83)^2}{6-1}} \\ =\sqrt[]{\frac{1276.2334}{5}} \\ =15.98 \end{gathered}[/tex]Therefore, the standard deviation of the data is 15.98
