Z-Score (Standard Score)
The Z-Score, also known as a Standard Score, is a statistic that tells us where a score lies in relation to the population mean. A positive Z-Score means that the score is above the mean, while a negative Z-Score means that the score is below the mean. In addition, the Z-Score also tells us how far the score is from the mean. It is a very useful statistic because it allows us to compare two scores coming from two different distributions.
For example, if you wanted to know how well you were performing in your Psychology class compared to your Philosophy class, you cannot simply compare your grades from the two classes, since each class is composed of a different population. So if you got a grade of 90 in Psychology and an 85 in Philosophy, it would not automatically mean that you were doing better in your Psychology class. If most of the Psychology students were getting scores in the 90s, then you might just be performing in the average range. If most of the Philosophy students were getting scores in the low 80s, then you might even be one of the top performers in that class. The only way to find out would be to convert each of your scores in the two classes into Z-Scores. Let's say you got a Z-Score of 1.0 in Psychology, and 1.2 in Philosophy. This would tell you that even if you got a lower score in Philosophy, you are actually performing better in that class compared to your Psychology class.