Given data $6,5,9,13,12,8,10$
Mean of the given data$(\bar{x})$
$=\frac{6+5+9+13+12+8+10}{7}$
$=\frac{63}{7}=9$
The deviation of the respective data from the mean i.e. $\left(x_{i}-\bar{x}\right)$ are
$6-9,5-9,9-9,13-9,12-9,8-9,10-9$
$\left(x_{i}-\bar{x}\right) =-3,-4,0,4,3,-1,1$
$\left(x_{i}-\bar{x}\right)^{2} =9,16,0,16,9,1,1$
$\displaystyle\sum_{i=1}^{7}\left(x_{i}-\bar{x}\right)^{2} =9+16+0+16+9+1+1$
$=52$
$\therefore $ Standard deviation $(\sigma)$
$=\sqrt{\frac{1}{n} \displaystyle \sum_{i=1}^{7}\left(x_{i}-\bar{x}\right)^{2}}=\sqrt{\frac{52}{7}}$