Understanding statistics associated with sampling

In the previous section, you saw something like a histogram plot of the samples' means. We used the histogram to show the quality of the sampled mean. If the distribution of the mean is centered around the true mean, I claim it has a better quality. In this section, we will go deeper into it.

Instead of using Texas population data, I will be using artificial uniform distributions as examples. It should be easier for you to grasp the quantitative intuition if the distribution underlining the population is clear.

Sampling distribution of the sample mean

You have seen the distribution of the sampled mean in the previous section. There are some questions remaining. For example, what is the systematic relationship between the sample size and the sample mean? What is the relationship between the number of times of sampling and the sample mean's distribution?

Assume we have a population that can only take values from...