The “preliminary terrors“, of course, being the notation as Silvanus P. Thompson so aptly described them :).
μ sounds like “mew”
σ sounds like “sigma”
x̄ sounds like “x-bar”
So we can think of this as the complete set of “things”, whatever the “things” are that are under consideration – for example if we’re interested in men’s heights in South Africa, then the population would be ALL men’s heights in South Africa. The notation looks like this:
The sample is a subset of the “things”under consideration – for example if we’re interested in men’s heights in South Africa, then the sample might be 100 men’s heights as measured in Cape Town. The notation looks like this:
Notice that although the symbols are different, the formulae are the same
When it comes to the central limit theorem and the z-score then we find some varieties of the above notation to represent accurately some different scenarios, like the mean of the sample means. x̄ is used to represent the sample means. The reason why we use μ to represent the mean is that it is the mean of ALL the sample means in our population of sample means! Once you can wrap your head around this, the notation is actually beautifully logical :).