X 3 6 9 12 15 P(X) 4/9 2/9 1/9 1/9 1/9

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$m e an = E (X) = \sum_{i} x_{i} p (x_{i})$

$=3(\dfrac{4}{9})+6(\dfrac{2}{9})+9(\dfrac{1}{9})+12(\dfrac{1}{9})+15(\dfrac{1}{9})$

$=\dfrac{20}{3}$

$E(X^2)=3^2(\dfrac{4}{9})+6^2(\dfrac{2}{9})+9^2(\dfrac{1}{9})+12^2(\dfrac{1}{9})$

$+15^2(\dfrac{1}{9})=62$

$Var(X)=\sigma^2=E(X^2)-(E(X))^2$

$=62-(\dfrac{20}{3})^2=\dfrac{158}{9}$

$\sigma=\sqrt{\sigma^2}=\sqrt{\dfrac{158}{9}}=\dfrac{\sqrt{158}}{3}\approx4.19$