This test has a standard deviation (σ) of 25 and a mean (μ) of 150.

Let’s assume that you have a test score of 190. Here’s a simple example so that you can easily determine the z score. The image below shows you the standard normal distribution when the mean is 0 and the standard deviation is 1.Īs you can see, you will need to first determine the difference between the raw score and the sample mean, and then divide the result by the sample standard deviation. The truth is that a z score also allows you to compare the scores of different variables by standardizing the distribution. To use a z score, you need to know not only the mean – μ, but also the population standard deviation – σ. On the other hand, when you get a negative value, it will be below the mean. In case you get a positive z score, then you know that the value is above the mean. It simply shows the position of the raw score in terms of the distance of this score from the mean when you measure it in standard deviation units. In addition, the standard deviation or variance will always be in increments of 1.Ī z score can be placed on a normal distribution curve. One of the things that you need to know about the z score is that when you calculate its mean, the result will always be 0. In case you are looking for a more technical definition, then we can say that the z score is a measure of how many standard deviations there are that are above or below the population mean. The z-score, which is also known as the standard score, is the number of standard deviations from the mean a data point is.

Distribution normal table