Alternative approach: if you know sum(xi) and sum($xi^2$) for each group, just add them. For groups with sums S1, S2 and sum-of-squares Q1, Q2 and sizes n1, n2: Combined sum = S1+S2, combined sum of squares = Q1+Q2, combined n = n1+n2. Then combined mean = $\frac{S1+S2}{(n1+n2)}$ and combined variance = $\frac{Q1+Q2}{(n1+n2)}$ - (combined mean)^2. This avoids the d1, d2 formula entirely.