# Standard Error - Why the calculation works

I'm new to statistics, and in an effort to understand how Standard Error works I've put together a small data set to try and get my head round it and would be really grateful if you could answer a question I have (unfortunately scouring the site did not enable me to answer my questions).

I've made a small population giving each value in the population a reference and calculated the population mean, variance and standard deviation below:

I then created a list of all possible samples that could be drawn from the population with a sample size of 3 (needless to say they didn't all fit in the image so this is a snapshot of them). I calculated each individual sample's mean (which from what I understand if I did a frequency plot of, would be a sampling distribution of the sample means), the variance and standard deviation.

At the top is the mean, variance and standard deviation based on all the sample means. The population mean is the same as the mean of all the sample means which is what I was expecting.

I know the equation for standard error is the sample standard deviation divided by the square root of the sample size, so in my example below Sσ/√n

My questions are:

Currently I am working standard error out on a sample per sample basis as you can see above, is this correct or should I be taking (in a hypothetical situation where I only have 10 of the samples to work with) the means of S1 to S10 designated Sσ in the example and diving that by the square root of the number of samples which would be 10?

Am I right in thinking the value arrived at for Standard Error is an estimate of the sampling distribution standard deviation (what I have called Dσ in my example above) or is it an estimation of the population standard deviation (what I have called Pσ in my population example above)?

Many Thanks!