What is the Z score formula used to standardize a value?

The Z score formula is used to standardize a value and provides a way to understand how far away a particular data point is from the mean of a given dataset, measured in terms of standard deviations. The correct formula is Z = (x - X) / SD, where "x" is the value being standardized, "X" represents the mean of the dataset, and "SD" is the standard deviation.

In this formula, you subtract the mean (X) from the value (x). This difference tells you how far the value is from the average. Dividing this difference by the standard deviation (SD) then normalizes the scale, placing the result in the context of the spread of the dataset. It helps in understanding if the value is above or below the mean and by how much, expressed in standard deviations.

This means a Z score of 0 indicates that the value is exactly at the mean, positive Z scores show the value is above the mean, and negative Z scores indicate the value is below the mean. Thus, using this standardization method helps in comparing different data points across various scales or distributions.