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I have the mean and standard deviation for Male and Female groups in a study, I'm trying to get the combined mean and standard deviation. The two groups have different N's. I can get the weighted average of the two means, but I don't know how to get the new standard deviation, given that the N's are different. Is there a modified version of Var(x+y)=Var(x)+Var(y) that takes into account the sample sizes too that I can use?

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