$\because$数据$a$，$4$，$2$，$5$，$3$的平均数为$b$，其中$a$，$b$是方程$x^{2}-4x+3=0$的两个根，
$\therefore \left\{\begin{array}{l}a+b=4\\ b=\frac{a+4+2+5+3}{5}\end{array}\right.$，
解得$\left\{\begin{array}{l}a=1\\ b=3\end{array}\right.$；
$\therefore$这组数据的标准差是$\sqrt{\frac{1}{5}[(1-3)^{2}+(4-3)^{2}+(2-3)^{2}+(5-3)^{2}+(3-3)^{2}]}=\sqrt{2}$；
故答案为：$\sqrt{2}$.

$\because$数据$a$，$4$，$2$，$5$，$3$的平均数为$b$，其中$a$，$b$是方程$x^{2}-4x+3=0$的两个根，
$\therefore \left\{\begin{array}{l}a+b=4\\ b=\frac{a+4+2+5+3}{5}\end{array}\right.$，
解得$\left\{\begin{array}{l}a=1\\ b=3\end{array}\right.$；
$\therefore$这组数据的标准差是$\sqrt{\frac{1}{5}[(1-3)^{2}+(4-3)^{2}+(2-3)^{2}+(5-3)^{2}+(3-3)^{2}]}=\sqrt{2}$；
故答案为：$\sqrt{2}$.