What is the formula for calculating a Z-score?

The formula for calculating a Z-score is expressed as z = (x - mean) / standard deviation. This formula is used to determine how many standard deviations a data point (x) is from the mean of the data set.

To break it down, the Z-score quantifies the position of a specific value (x) relative to the average (mean) of the data set, considering the spread of the data represented by the standard deviation. When you subtract the mean from the data point, you're finding the difference between the value and the average, which helps in understanding whether the value is above or below the mean. Dividing this difference by the standard deviation normalizes this difference, giving you the Z-score that indicates the relative standing of the value in the context of the overall distribution of the data.

This provides a standardized way to compare values from different distributions or different scales, making it a useful tool in statistics for identifying outliers or for various inferential statistics.