Understanding Z-Scores
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. Z-scores are measured in terms of standard deviations from the mean. Our free Z-Score Calculator allows you to quickly standardize raw data and calculate probabilities for normal distributions.
If a Z-score is 0, it indicates that the data point's score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean.
The Z-Score Formula
The formula to calculate a Z-score requires the raw score, the population mean, and the population standard deviation:
Z = (X - μ) / σ
- Z = The Z-score (Standard Score)
- X = The Raw Score (the value you are evaluating)
- μ (Mu) = The Population Mean
- σ (Sigma) = The Population Standard Deviation
Why use a Standard Score?
Z-scores are incredibly useful because they allow you to compare results from completely different tests or surveys. By converting raw data into standardized scores, you can map them onto a standard normal distribution.
For example, comparing a score on the SAT to a score on the ACT is difficult because they use different scales. By converting both to Z-scores, you can easily determine which test performance was statistically better relative to the average test-taker.