Try the Live Calculator ⮕
What is a Z-Score?
A Z-score (also known as a standard score) is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.
The Z-Score Formula
To calculate a Z-score, you subtract the population mean from an individual raw score and then divide the difference by the population standard deviation:
Key Components for Calculation
- Raw Score (x): The specific value you want to standardize.
- Population Mean (μ): The average value of the entire dataset.
- Standard Deviation (σ): The measure of the amount of variation or dispersion in the set.
- Z-Score (z): The result, telling you how many standard deviations the score is above or below the mean.
Why Use Z-Scores?
Z-scores allow statisticians to compare data points from different datasets that have different means and standard deviations. For example, you can use Z-scores to compare a student's performance on an SAT exam with their performance on an ACT exam, even though the scoring scales are completely different.