# About sample mean and the mean of various samples

What I would like to know it is the precise use of both statistics -- the sample mean and the mean of various samples. I'm getting a bit confused with the notation in my textbook and sometimes I cannot make a clear distinction between both statistics. For instance, when we talk about "Xi" (i=1,2...) aleatory variables from one population that approaches a normal distribution, I can assume we are talking about various samples from one population that approaches a normal distribution? I would be glad if someone could give me a clear difference in the use of both statistics (it would be nice a distinction of the variance in both approaches too) and its properties.

Thanks o/

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