What does a z-score indicate?

A z-score is a statistical measurement that describes how far away a specific data point is from the mean of a dataset, measured in terms of standard deviations. When you calculate a z-score, you essentially determine the number of standard deviations a data point is from the average value of the dataset. This is useful in identifying outliers and understanding the relative position of a data point within a distribution.

Thus, when the correct answer indicates that a z-score reflects the distance a sample is above or below the mean, it captures the essence of how a z-score is used in statistics. A positive z-score signifies that the data point is above the mean, while a negative z-score indicates it is below the mean. This quantifies the position of the data point within the context of the overall data distribution and provides insight into how typical or unusual that point is compared to the average.

The other options do not accurately describe the function of a z-score. For example, a z-score does not represent the proportion of data in a distribution, nor does it define the strength of a relationship between variables. Additionally, while z-scores are related to standard deviation, they do not indicate the standard deviation of a sample directly; rather, they are calculated using the standard deviation