Variance measures the spread of data around its mean. Two equivalent formulas: $sigma^2$ = sum(xi - x-bar)^2/n (definitional) and $sigma^2$ = sum$\frac{xi^2}{n}$ - (x-bar)^2 (computational). The computational formula is faster and is the primary tool for JEE. For frequency data: $sigma^2$ = sum$\frac{fi*xi^2}{N}$ - $\frac{sum(fi*xi}{N}$)^2. Variance is always non-negative and equals zero only when all observations are identical. Its unit is the square of the data's unit. Standard deviation sigma = sqrt(variance) restores the original unit. The variance formula can be rewritten as: n*$sigma^2$ = sum($xi^2$) - n*(x-bar)^2, which means sum($xi^2$) = n*($sigma^2$ + x-$bar^2$). This rearrangement is crucial for "corrected variance" problems where you need to recover sum($xi^2$) from given mean and variance.