# Z-Score (Standard Score)

**Formula:** `Z = (X - μ) / σ`

The Z-score, or standard score, is a numerical measurement that describes a value's relationship to the mean of a group of values. It is calculated using the formula ** Z = (X - μ) / σ**, where

**is the value in question,**

*X***is the mean of the data set, and**

*μ***is the standard deviation. This score indicates how many standard deviations an element is from the mean. A positive Z-score means the value is above the mean, while a negative Z-score indicates it is below the mean.**

*σ*The Z-score is useful in statistics for standardizing different data sets to be compared on common terms, for identifying outliers, and for calculating probabilities in a normal distribution. For instance, Z-scores are used in standardizing test scores to account for varying difficulty levels, or in finance to measure the performance of an investment relative to its risk.

Tags: Statistics, Standardization, Normal Distribution, Score