Use $E(X)=\sum x p$ and $\operatorname{Var}(X)=E(X^2)-[E(X)]^2$ with $E(X^2)=\sum x^2 p$.

$E(X)=2.7$, $E(X^2)=8.1$, so $\operatorname{Var}(X)=8.1-2.7^2=0.81$ and $\sigma=0.9$.

Build the products $x p$ and $x^2 p$ column by column.

Mean. $E(X)=\sum xp = 0.1+0.6+1.2+0.8 = 2.7.$

Variance. $E(X^2)=\sum x^2 p = 0.1+1.2+3.6+3.2 = 8.1$, so

Standard deviation. $\sigma=\sqrt{0.81}=0.9.$

Independent check (definition of variance). Using $\operatorname{Var}=\sum (x-\mu)^2 p$ with $\mu=2.7$: deviations $-1.7,-0.7,0.3,1.3$ give squared deviations $2.89,0.49,0.09,1.69$; weighting: $2.89(0.1)+0.49(0.3)+0.09(0.4)+1.69(0.2)=0.289+0.147+0.036+0.338=0.81$ — matches.

The two-column table ($xp$ and $x^2p$) is the fastest reliable layout; then $\operatorname{Var}=E(X^2)-[E(X)]^2$ needs only the two totals.

Computing $\operatorname{Var}=E(X^2)-E(X)$ instead of $E(X^2)-[E(X)]^2$ — the mean must be squared before subtracting. Also forgetting to take the square root for the standard deviation.