Suppose we draw a sample $x$ from a population $X$,  this sample has $n$ random variables $(x_1, x_2, x_3... x_n)$, the sample mean is $\bar{x}$, and it's variance is $v(x)$,  the whole population is $X$, has a mean is $\mu$ , variance $V(X) = \sigma^2$, 

say this specific sample mean $\bar{x}$ follows a sampling distribution $W$, the variance of this $\bar{x}$ is $V(\bar{x})$.

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

are $V(x)$ and $V(\bar{x})$ exactly the same?

we know that $V(\bar{x}) = \sigma^2 /n$

but is $V(x)$  also equal to  $\sigma^2 /n$?


please notice $V(X)$ and $V(x)$ and $V(\bar{x})$ has three total different meaning:

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