Z-Score Calculator
Calculate the z-score (standard score) of a value given the mean and standard deviation.
The Z-Score Calculator determines how many standard deviations a value is from the mean. A z-score of 0 means the value equals the mean, positive means above, and negative means below.
Enter a data value, the population mean, and the standard deviation. The calculator uses the formula z = (x - mean) / std_dev to compute the standard score.
Z-scores are fundamental in statistics for comparing values from different distributions, identifying outliers, and performing hypothesis testing. About 68% of values fall within z = +/-1, 95% within z = +/-2, and 99.7% within z = +/-3 (the empirical rule).
Frequently Asked Questions
What does a z-score tell you?
A z-score tells you how many standard deviations a value is from the mean. Z = 2 means the value is 2 standard deviations above the mean.
What is considered an unusual z-score?
Values with z-scores beyond +/-2 are often considered unusual (only ~5% of data), and beyond +/-3 are very rare (~0.3%).
How are z-scores used in grading?
Z-scores standardize test results across different exams, allowing fair comparison. A z-score of 1.5 on any test means you scored 1.5 std devs above average.