What is the formula for the z-score?

The formula for the z-score is defined as Z = (X - μ) / σ, where X represents a particular value from the dataset, μ is the mean of the dataset, and σ is the standard deviation.

This formula provides a standardized way to determine how far a specific value (X) deviates from the average (the mean, μ) by scaling this deviation with the standard deviation (σ).

A positive z-score indicates that the value is above the mean, while a negative z-score suggests it is below the mean. The magnitude of the z-score reflects how many standard deviations away from the mean the value lies. This is crucial for identifying outliers and understanding the position of data points within a normal distribution.

The other formulations incorrectly manipulate the parameters or misrepresent the relationships necessary for calculating the z-score, failing to adhere to the statistics definitions and principles behind standardization.