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.
