Variance of the Sampling Distribution of the Sample Mean

CFA Level I Quant
#1

Hi all, I can’t seem to wrap my head around a concept for sampling dist.

As we know the sampling dist for the sample mean is normally distributed as ~(population mean, σ^2/(n)).

I can’t seem to understand why would the variance of the sampling dist NOT be the VAR(sample means) (eg. sum of (individual sample mean - mean of the sample means)^2/n).

Thanks in advance!

#2

Means of a bunch of observations are not as widely distributed as the observations themselves are.

Grab two giraffes at random and measure their heights; how different are they from each other?

Take two random samples of 500 giraffes and compute their mean heights; how different are those two from each other?

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