Hi I have an exam this friday. Covering normal frequency distribution chart/graph, variance, standard deviation, and z-scores?

So my question is there is that formula for standard deviation/variance. the s or s^2 is when we are using data from a sample and then on the bottom the formula will be /n-1 . on a population we use thetta or thetta^2, and N on the bottom only.

My question is to get variance we just plug in data value + mean, and we get the variance in the square root. then if we square it, we get the standard deviation.

What does variance mean on a chart or in practical use.

Doesn't standard deviation represent the z-scores, in that, the middle will be 34.1 percent x2, which equals 68.2 percent of 1 standard deviation of the graph, then the next will be 13.1, which is 26.2, which 26.2+68.2, is 2 standard deviation, then the rest are considered outliers, or "unlikely"? So I could see what that means with data value.

However, standard deviation is practically just dispersion of the data? How far apart we are from the next section or group? What does the variance do then? Also, how do I correlate standard variation with z-scores on a graph?