Question about the spread of the sampling distribution

Quote:

Originally Posted by funnyname7

The spread of the sampling distribution of sample means will always be smaller than the spread of the distribution of the population (n=2 or more).

True or False.

I said true because with a lot of samples –μx = μ, and σx is smaller than σ (the distribution less spread out).

If the population variance (and so standard deviation) exist then:

The variance of the sample mean is $\sigma^2/N$ where $\sigma^2$ is the population variance and $N$ the sample size.

So the variance of the sample mean is smaller than the variance of the population and so the same goes for standard deviations.

Now if by spread you mean SD then the answer is yes.

However if the population variance does not exist, the sample mean also does not have a variance and so the answer is no.

CB