What does a z-score represent?

A z-score is a statistical measurement that indicates how many standard deviations a particular data point is away from the mean of the dataset. This means that a z-score provides insight into the relative position of the data point within the context of the entire distribution.

When the z-score is calculated, a positive value signifies that the data point is above the mean, while a negative value indicates that it is below the mean. The z-score is a crucial concept in standardization, allowing for comparison between different datasets that may have different means and standard deviations. By transforming scores into z-scores, researchers can interpret how unusual or typical a particular score is within the larger dataset.

This understanding is fundamental in statistics, especially when conducting hypothesis testing or assessing normality, as it provides a clear metric for determining the likelihood of occurrence of a specific value based on the properties of the normal distribution.