What is the formula for calculating a z-score?

The formula for calculating a z-score is z = (score - mean) / standard deviation. This formula measures how many standard deviations an individual score is from the mean of the distribution.

In this context, "score" refers to the value for which you are calculating the z-score, "mean" is the average value of the dataset, and "standard deviation" indicates the amount of variation or dispersion of the scores in that dataset.

By subtracting the mean from the score, you determine the deviation of the score from the average. Dividing this difference by the standard deviation standardizes this deviation, allowing you to understand it in the context of the data's variability. A positive z-score indicates that the score is above the mean, while a negative z-score indicates that it is below the mean. This transformation is essential for various statistical analyses and for comparing scores from different distributions.