I'm currently learning about basic statistics and the sampling distribution. You'll have to forgive my misuse of terms as I'm still learning. My question is about how is the average of a population the same as the average of the sampling distribution.
I'll go through my understanding and have done a basic example to try and illustrate, please correct me if I'm wrong.
My understanding is if I have a set of values below - the population:
Then given a sample size, the sampling distribution is a histogram of the averages of all possible combinations able to be drawn from the population.
For example with a sample size of 2 using the set of values above as the population there are total of 6 possible samples able to be drawn. With a sample size of 3 there are 4 possible samples able to be drawn, as shown below:
I'm aware this may be a little ahead of my ability to understand, but wondered if someone could help trace through how the mean of a set of values is the same as the mean of all the possible sample means.