The size of the data set—the sample size—doesn't affect standard deviation, but the sample size is a key factor in calculating the SEM. A larger random sample will always provide a mean that ...

The normal distribution formula is based on two simple parameters—mean and standard deviation—that quantify the characteristics of a given dataset.

Most succinctly put, standard deviation is about where the data are clustered in one sample data, while SEM is where the means would be clustered around many samples taken of a given set of things ...