[tex]5;\ 5;\ 5;\ 5;\ 7;\ 9\\\\\overline{x}=\dfrac{5+5+5+5+7+9}{6}=\dfrac{36}{6}=6\\\\\delta^2=\dfrac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+(x_3-\overline{x})^2+...+(x_n-\overline{x})^2}{n}\\\\\delta^2=\dfrac{(5-6)^2+(5-6)^2+(5-6)^2+(5-6)^2+}{6}[/tex]
[tex]\dfrac{+(7-6)^2+(9-6)^2}{6}\\\\\delta^2=\dfrac{(-1)^2+(-1)^2+(-1)^2+(-1)^2+1^2+3^2}{6}=\dfrac{14}{6}=\dfrac{7}{3}[/tex]
[tex]standard\ deviation:\\\\\sqrt{\delta^2}=\sqrt{\dfrac{7}{3}}=\dfrac{\sqrt7}{\sqrt3}=\dfrac{\sqrt7\cdot\sqrt3}{\sqrt3\cdot\sqrt3}=\boxed{\dfrac{\sqrt{21}}{3}}\approx\boxed{1.53}[/tex]
