For grouped data, variance and standard deviation are computed by weighting each squared deviation by its frequency: $\sigma^2=\dfrac1N\sum f_i(x_i-\bar x)^2$, where $x_i$ is the value (discrete distribution) or class midpoint (continuous distribution) and $N=\sum f_i$. The computational shortcut extends directly, $\sigma^2=\dfrac1N\sum f_ix_i^2-\bar x^2$, needing only the two running totals $\sum f_ix_i$ and $\sum f_ix_i^2 …