What information does calculating standard deviation provide? How is the z-score related to standard deviation? Solution Part 1: In statistics and probability theory, standard deviation shows how much variation or \"dispersion\" exists from the average (mean, or expected value). A low standard deviation indicates that the data points tend to be very close to the mean; high standard deviation indicates that the data points are spread out over a large range of values. Part 2: A Z-Score is a statistical measurement of a score\'s relationship to the mean in a group of scores. A Z-score of 0 means the score is the same as the mean. A Z-score can also be positive or negative, indicating whether it is above or below the mean and by how many standard deviations. The z score is how many standard deviations from the mean that your data was..