What is the z-score in relation to a normal distribution?

The z-score is fundamentally a measure that indicates how many standard deviations a particular data point is from the mean of a distribution. It is calculated by taking the difference between the score and the mean, then dividing that difference by the standard deviation of the distribution. This process effectively standardizes different scores onto a common scale, enabling comparisons across different datasets or distributions.

When you apply the concept of z-scores to a normal distribution, it transforms the original scores into a standardized format that allows one to determine the relative position of a score within the overall data set. A z-score of 0 means the score is exactly at the mean, while positive or negative z-scores indicate how many standard deviations above or below the mean a score lies, respectively.

In contrast, measures of central tendency focus on summarizing data with values like the mean or median, methods of data visualization encompass tools such as graphs or charts, and measures of sample variability pertain to statistics such as variance and standard deviation that describe how spread out the data points are. None of these capture the specific role of a z-score in standardizing scores in relation to a normal distribution.