What Is a Z-Score and Why It Matters
A z-score, also known as a standard score, describes how far a specific value is from the mean of a dataset, measured in units of standard deviation. It allows values from different datasets to be compared on a common scale.
Z-scores are widely used in statistics, standardized testing, psychology, finance, and quality control. They help identify whether a value is typical, unusually high, or unusually low compared to the rest of the data.
Z-Score Formula
In this formula, x is the observed value, μ is the mean, and σ is the standard deviation. A positive z-score means the value is above the mean, while a negative z-score indicates the value is below the mean.
Example Interpretation
If a test score has a z-score of 1.5, it means the score is 1.5 standard deviations above the mean. If the z-score is −2, the score is two standard deviations below the mean.
Z-scores near zero indicate values close to the mean, while large positive or negative z-scores may indicate outliers or exceptional cases.
When to Use Z-Scores
Z-scores are especially useful when comparing values from different distributions, such as exam scores from different classes or performance metrics across groups. They are also used in probability calculations involving the normal distribution.