I really need to redo this video. :/ The introduction of "What happens if we repeatedly sample...." sounds confusing because you DON'T repeatedly sample. The phrase should be "What WOULD happen if we WERE to repeatedly sample....." . I simulated repeated sampling in the video to try to develop the idea of the sample average changing. In the "real world" you don't need to repeated sample. You take one sample. The key is to think about a sample average (x-bar) as a variable. It changes because every sample is likely to be a unique group of individuals and so the average of a sample from a given population would likely be different with every new sample. This video does something the book doesn't as well, which is use subscripts to indicate whether we are referring to one thing at a time (x) or the sample average ("xbar"..looks like an 'x' with a line over it). For example, if the variable is "adult female heights", I will use (mu_x and sigma_x....the 'x's being the subscripts) to refer to the average height of one female. If sigma_x = 5 inches, that describes the variability of the height of measuring one female at a time. ("Mu" is the greek letter that looks like a cursive "u" and "sigma" is the greek letter that looks like an "o" with a line coming out the top of it) "The Sampling Distribution of X-Bar" refers to the changing nature of the average height of a group of females. The symbols for describing the mean and standard deviation of this distribution are mu_xbar and sigma_xbar. The big thing is that the VARIABILITY of the sample mean is always LESS than for one individual. As as example, suppose you plan to measure the heights of 40 adult females. Is seems relatively likely that one person in that group will be over 6 ft tall. That is because the distribution of the height of one person is relatively spread out. But if you ask yourself "How likely is it that THE AVERAGE HEIGHT of those 40 females as a group is more than 6 feet tall?"...Well that is much less likely. You'd need a group of 40 women that are generally a decent amount taller than average, which is just pretty rare. What this idea looks like with numbers, is that if sigma_x=5 inches (the variability of one person)...then sigma_xbar (the variability of your sample average of 40 people) is given by sigma_xbar= = (sigma_x)/(the square root of the sample size) = (sigma_x)/sqrt(n) = 5/sqrt(40) = 5/6.32 = 0.790 inches. This is the variability of the sample mean. It is less than one inch. *The sample mean has less variability than individual values.* Interestingly, the center of the distributions of individuals and the sample mean are the same. mu_x = mu_xbar. If the average height of adult females is 67 inches (mu_x=67), the distribution of the sample mean will be centered on that same value of 76. (mu_xbar = 67).... Summarizing....For this female heights example, The distribution of the height of one female (x) Its shape is Normal Its center is mu_x = 67 inches Its variability is mu_x = 5 inches The (sampling) distribution of the average height of 40 females (x-bar....when n=40) Its shape is Normal Its center is mu_xbar = 67 inches Its variability is mu_xbar = 0.79 inches Hope that helps!