Why use this calculator
Z-scores standardize data points so you can compare values from different distributions and determine how unusual a value is.
How to use it
Enter the data point, population mean, and standard deviation. The calculator shows how many standard deviations away from the mean your value is.
The formula
Z = (X - μ) / σ. The Z-score tells you how many standard deviations above or below the mean a value falls.
Worked examples
Score of 85 with mean 75 and SD 10
Z-score = 1.0, about 84th percentile
When people use it
- Academic grading curves
- Quality control
- Statistical testing
- Comparing scores across different scales
Tips
- Z-scores between -2 and 2 cover about 95% of data in a normal distribution
- A Z-score of 0 means the value equals the mean
Questions people ask
- What does a Z-score of 2 mean?
- It means the value is 2 standard deviations above the mean. In a normal distribution, only about 2.3% of values are this high or higher.