Given:
A sample data is,
13,5,25,16,21.
First, calculate the mean of the data,
[tex]\begin{gathered} \bar{x}=\frac{13+5+25+16+21}{5} \\ =\frac{80}{5} \\ =16 \end{gathered}[/tex]The standard deviation is calculated as,
[tex]\begin{gathered} s^2=\frac{\sum^{}_{}(x_i-\bar{x})^2}{N-1} \\ N=5\text{ =number of data points} \\ s^2=\frac{(13-16)^2+(5-16)^2+(25-16)^2+(16-16)^2+(21-16)^2}{5-1} \\ s^2=\frac{236}{4} \\ s=\sqrt[]{59} \\ s=7.7 \end{gathered}[/tex]Answer: standard deviation is 7.7
