Z Score Calculator
Calculate a z score using a value, mean, and standard deviation. A z score shows how far a value is from the mean in standard deviation units.
Enter the data point you want to evaluate.
Enter the mean of the data set.
Enter the standard deviation of the data set.
How This Calculator Works
A z score measures how far a value is from the mean of a data set. The result is expressed in standard deviation units. Positive z scores are above the mean, negative z scores are below the mean, and a z score of 0 means the value is exactly at the mean.
Formula
Z Score = (Value - Mean) / Standard Deviation
Example
If a test score is 85, the class mean is 70, and the standard deviation is 10, the z score is 1.5. That means the score is 1.5 standard deviations above the mean.
Frequently Asked Questions
What does a z score mean?
A z score shows how many standard deviations a value is above or below the mean.
What does a positive z score mean?
A positive z score means the value is above the mean of the data set.
What does a negative z score mean?
A negative z score means the value is below the mean of the data set.
What does a z score of 0 mean?
A z score of 0 means the value is exactly equal to the mean.
Why must standard deviation be greater than 0?
Standard deviation cannot be 0 in this formula because dividing by 0 is not valid.