Combined Variance of Two Sets

Rarely Tested

$$\sigma_c^2 = \frac{n_1(\sigma_1^2 + d_1^2) + n_2(\sigma_2^2 + d_2^2)}{n_1 + n_2}$$

Where $$d_1 = \bar{x}_1 - \bar{x}_c$$, $$d_2 = \bar{x}_2 - \bar{x}_c$$,
$$\bar{x}_c = \frac{n_1\bar{x}_1 + n_2\bar{x}_2}{n_1 + n_2}$$,
$$n_1, n_2$$ = sizes, $$\sigma_1^2, \sigma_2^2$$ = variances.

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