When merging two groups: combined mean x-bar = $\frac{n1*x1-bar + n2*x2-bar}{(n1+n2)}$. Combined variance uses the formula: $s^2$ = [n1*(s1^{2+d1}^2) + n2*(s2^{2+d2}^2)]/(n1+n2), where di = xi-bar - x-bar (deviation of each group mean from combined mean). Intuition: the combined variance has two components — the within-group variance ($s1^2$, $s2^2$) and the between-group variance ($d1^2$, $d2^2$). Even if both groups have zero variance individually, the combined variance is nonzero if their means differ. Shortcut: if both groups have the same mean, combined variance = $\frac{n1*s1^2 + n2*s2^2}{(n1+n2)}$. Alternatively, add raw sums: combined sum = S1+S2, combined sum of squares = Q1+Q2, then use the computational formula.