When merging two groups: combined mean x-bar = (n1x1-bar + n2x2-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 = (n1s1^2 + n2s2^2)/(n1+n2). Alternatively, add raw sums: combined sum = S1+S2, combined sum of squares = Q1+Q2, then use the computational formula.