Jack lists all of the unique random samples of a certain sample size from a population. He then calculates the mean for each of these unique random samples. Finally, he calculates a standard deviation of all the sample means. What is the correct notation and name for this standard deviation?

In this case Jack is only using a part or sample of the total population, so he is doing a sample standard deviation. When you use the total population you are doing a population standard deviation, otherwise, it's always going to be the sample standard deviation.

Both deviations have different notations. The notation for this type of standard deviation (the one used by Jack) is:

"n" for the number of observations (lowercase)

"x-bar" for the average of the sample

"s" for the standard deviation

"s^2" for the variance