## What is Z-score?

Z-score is a statistical measurement representing the value’s relationship to the mean. It denotes the number of standard deviations a given data point lies above or below the mean.

## Z-score Formula

Z-score is calculated using the standard deviation and the mean of the group.

z-score =

where,

**μ** = mean

**σ **= standard deviation

**x **= current value

## Value of Z-score

**z-score >0, positive z-score**

It represents a value greater than the mean.**z-score<0, negative z-score**

It represents a value less than the mean.**z-score == 0, zero z-score**

It represents a value equal to the mean.

## Applications of Z-score

Below are a few applications of the Z-score:

**1. Outlier Detection**

Z-score can be used to detect outliers. A value is considered an outlier if :

**z-score > +3****z-score < -3**

**2. Normal Distribution to Standard Normal Distribution**

Z- score is used to convert the normal distribution into the standard normal distribution.

**Standard Normal Distribution**

It is a special type of normal distribution where the **mean is 0** and the **standard deviation is 1**.