deletions | additions       diff --git a/Computing_this_within_class_variance__.tex b/Computing_this_within_class_variance__.tex  index d6fdd0f..be888a2 100644  --- a/Computing_this_within_class_variance__.tex  +++ b/Computing_this_within_class_variance__.tex 
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\begin{align}  \sigma_{\text{Between}}(T) &= \sigma^2 - \sigma^2_{\text{Within}}(T) \\  & = n_B(T)[\mu_B(T)-\mu]^2+n_O(T)[\mu_O(T)-\mu]^2  \end{align} where \sigma^2 is the combined variance and \mu is the combined mean. Notice that the between-class variance is simply the weighted variance of the cluster means themselves around the overall mean. Substituting $\mu = n_B(T)\mu_B(T)+n_O(T)\mu_O(T)$ and simplifying, we get  $$\sigma^2_{\text{Between}}(T) = n_B(T)n_O(T)[\mu_B(T)-\mu_O(T)]^2$