What does a Z-score indicate in a statistical distribution?

A Z-score is a statistical measurement that indicates how many standard deviations a particular score is from the mean of the dataset. It provides a way to understand the relative position of a specific value within the context of the entire distribution. When a Z-score is calculated, it tells us whether the score is above or below the mean and how far away it is in terms of standard deviations.

This concept is particularly useful when comparing scores from different distributions, as Z-scores normalize values, allowing for a direct comparison regardless of the original units or scales of the data. For instance, if a Z-score is +1, it indicates that the score is one standard deviation above the mean; conversely, a Z-score of -2 means the score is two standard deviations below the mean. This normalization is crucial in statistical analysis and hypothesis testing, enabling researchers to assess the significance of their findings in a standardized manner.