A Z-score is a standardized score that can be used to compare distributions that are quite different. The unit for the z-score is a standard deviation, and the z-score can be used to calculate the probability of having a score that distance from the mean (Salkind, 2017).

I created this fictional data set to use in a demonstration of how to calculate z-scores. The scores represent the scores on the Stanford-Binet IQ test. The mean score of the general population is 100 with a standard deviation of 15.

In this scenario the school wants to see if the IQ scores of the students enrolled in the class are higher than the general population.