📐 Math
Z-Score Calculator
Calculate the standard score (z-score) which represents how many standard deviations a raw score is above or below the mean of a population.
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Formula
z = (x - μ) / σx- Raw score
μ- Population mean
σ- Population standard deviation
Example
Standardizing a Test Score
You scored 85 on a test. The class average was 75 with a standard deviation of 5. Find your z-score.
- Set x = 85 (your score).
- Set μ = 75 (the mean).
- Set σ = 5 (the standard deviation).
- Subtract the mean from your score: 85 - 75 = 10.
- Divide by the standard deviation: 10 / 5 = 2.
- Result: Your z-score is 2 (you are 2 standard deviations above the mean).
Frequently Asked Questions
A negative z-score means the raw score is below the average (mean). A z-score of 0 means the score is exactly equal to the mean.