What is a Z-Score?
A Z-score (also called a standard score) measures how many standard deviations a data point is from the mean of a dataset. It’s a statistical measurement that describes a value’s relationship to the mean of a group of values.
Z = (X – μ) / σ
Where:
- Z is the Z-score
- X is the value being measured
- μ (mu) is the mean of the population
- σ (sigma) is the standard deviation of the population
Interpretation
A Z-score of 0 indicates the data point is exactly at the mean. A positive Z-score indicates the data point is above the mean, while a negative Z-score shows it’s below the mean.
Examples
Z = 1.0: One standard deviation above the mean
Z = -1.5: 1.5 standard deviations below the mean
Z = 2.0: Two standard deviations above the mean
Calculator
Result
Z-Score:
0.00
The data point is exactly at the mean.