Calculate the mean (E(X)).

The mean (or expected value) is calculated using the formula $E(X) = \sum x \cdot p(x)$.

$$E(X) = (3 \times 0.2) + (8 \times 0.7) + (10 \times 0.1)$$ $$E(X) = 0.6 + 5.6 + 1.0$$ $$E(X) = 7.2$$

The mean is $\boxed{7.2}$.

This is needed for the variance calculation. The formula is $E(X^2) = \sum x^2 \cdot p(x)$.

$$E(X^2) = (3^2 \times 0.2) + (8^2 \times 0.7) + (10^2 \times 0.1)$$ $$E(X^2) = (9 \times 0.2) + (64 \times 0.7) + (100 \times 0.1)$$ $$E(X^2) = 1.8 + 44.8 + 10.0$$ $$E(X^2) = 56.6$$

The variance is calculated using the formula $Var(X) = E(X^2) - [E(X)]^2$.

$$Var(X) = 56.6 - (7.2)^2$$ $$Var(X) = 56.6 - 51.84$$ $$Var(X) = 4.76$$

The variance is $\boxed{4.76}$.

The standard deviation is the square root of the variance.

$$\sigma_X = \sqrt{Var(X)}$$ $$\sigma_X = \sqrt{4.76}$$ $$\sigma_X \approx 2.1817$$

The standard deviation is $\boxed{2.18}$ (rounded to two decimal places).

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