supposed we draw a sample x from a population X,  this sample has n random variables (x1, x2, x3... xn), the sample mean is x̄, and it's variance is v(x),  the whole population is X, has a mean is μ , variance V(X) = σ, 

say this specific sample mean x̄ follows a sample distribution W, the variance of this x̄ is V(x̄).

and the variance of this specific sample is V(x),

are V(x) and  V(x̄) exactly the same?

we know that V(x̄) = σ*σ /n

but is V(x)  also equal to σ*σ /n??????


please notice V(X) and V(x) and V(x̄) has three total different meaning:

V(X) is the real variance of the whole population,
V(x) is the variance of one specific sample.
V(x̄) is the sample mean, when we change the sample, this sample mean changes too, and this changed sample mean follows a specific distribution W