Z-Score Calculator

Z-Score Calculator

The Z-score expresses how many standard deviations a data point sits away from the mean of its distribution - a standardized way to compare values across datasets measured on entirely different scales.

Z = (Value - Mean) / Standard Deviation

Example

A test score of 85, with a class mean of 70 and standard deviation of 10:

Z = (85 - 70) / 10 = 1.5 (1-2 standard deviations from the mean - somewhat unusual)

Interpreting the Score

|Z-score|	Interpretation
< 1	Typical, within 1 standard deviation
1-2	Somewhat unusual
2-3	Unusual
> 3	Strong outlier

Use in Data Science

Z-scores are used both for flagging outliers in a dataset and as a feature scaling technique (called standardization) that rescales every feature to have a mean of 0 and standard deviation of 1 - this matters enormously for distance-based algorithms like k-nearest neighbors, and for gradient-based models where features on wildly different scales can slow or destabilize training.