# Z-Score

## 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

1. z-score >0, positive z-score
It represents a value greater than the mean.
2. z-score<0, negative z-score
It represents a value less than the mean.
3. 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.