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(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(fixi^2)/N - (sum(fixi)/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: nsigma^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.