We have the following data
[tex]24,7,26,5,13[/tex]The standard deviation is given by
[tex]\sigma=\sqrt[]{\frac{\sum(x_i-\mu)^2}{N}}[/tex]Where μ is the mean and N is the number of data points
Let us first find the mean of the data.
[tex]\mu=\frac{\text{sum}}{number\text{ of data points}}=\frac{24+7+26+5+13}{5}=\frac{75}{5}=15[/tex]Finally, the standard deviation is
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(24-15)^2+(7-15)^2+(26-15)^2+(5-15)^2+(13-15)^2}{5}} \\ \sigma=\sqrt[]{\frac{(9)^2+(-8)^2+(11)^2+(-10)^2+(-2)^2}{5}} \\ \sigma=\sqrt[]{\frac{81^{}+64^{}+110^{}+100^{}+4^{}}{5}} \\ \sigma=\sqrt[]{\frac{359}{5}} \\ \sigma=\sqrt[]{71.8} \\ \sigma=8.5 \end{gathered}[/tex]Therefore, the standard deviation of the data set is 8.5
