How to estimate the variance of several populations when every population mean and variance is different?

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I'm currently using the Pooled Variance method, but in my case I cannot assume that every population variance is the same.

Is there a method for these cases ?

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Here's what I would try. Find estimates of $E[X^2]$ for each group and then an overall estimate using a weighting scheme by group count. Do the same for the mean. Then estimate the overall variance with $$\hat \sigma^2=E[X^2]-(E[X])^2.$$