When calculating Z scores, what does the numerator represent?

The numerator in the calculation of Z scores represents the difference between the raw score and the mean. This component is critical as it quantifies how far and in what direction the raw score is from the average of the dataset. By taking the raw score and subtracting the mean, you obtain a value that indicates whether the raw score is above or below the mean, and by how much.

This difference is then standardized by dividing it by the standard deviation, which is what allows the Z score to be interpreted as a standardized score reflecting how many standard deviations away from the mean the raw score is. Understanding this relationship is essential in various statistical analyses, as it facilitates the comparison of scores from different distributions on the same scale.