Variance of sample mean

[afterworkguinness]

Hi,
I'm not clear on what the "variance of the sample mean" is. Is it the variance of the sampling distribution ?

 

[David Harper CFA FRM]

Hi afterworks, Yes, that is correct. "Sampling distribution" refers to the probability distribution of an estimator (statistic) so we could refer to the sample distribution of a sample variance, or sample skew or any sampling statistic. Including, here, we often refer to the variance of [the sampling or probability distribution of] the sample mean.

To me, the key is to realize the sample mean is just one instance: it changes with each sample so it itself a random variable which can be characterized by a "sampling distribution"

For example, if you roll 10 six-sided die, maybe the average is 3.6; i.e., not exactly the population or "true" mean of 3.5, but as an estimate we expect it to be nearby. Roll all ten again, maybe you get an average of 3.4, and so on

so you end up with a sampling distrubution: {average of 3.6, 3.4, average in 3rd roll of 10 die, average in 4th roll of 10 die, etc} . The variance of the sample mean is the variance of this distribution. CLT says it will be approximately normal with variance of (population's variance)/10, regardless of the fact that the die has a non-normal (uniform) distribution. I hope that helps,

 

[afterworkguinness]

Great, thanks for clearing that up.