Step 1: Identify what's given — usually sum(xi), sum($xi^2$), n, mean, or variance. Step 2: Use the computational formula $sigma^2$ = sum$\frac{xi^2}{n}$ - (mean)^2 in both directions: given variance and mean, recover sum($xi^2$); given sums, compute variance. Step 3: For correction problems, adjust sums directly. Step 4: For transformation problems, apply the property: Var(a+bX) = $b^2$*Var(X). Step 5: For combined groups, either use the combined variance formula or add raw sums. Common mistakes: confusing SD with variance in transformation problems (SD scales by |b|, variance by $b^2$), forgetting to square the mean in the computational formula, and changing n when the observation is corrected (not removed). Time allocation: 2-3 minutes for direct computation, 3-4 for correction or combination problems.