Z-Score Formula
The formula to convert x to z is the following:
z = (x - μ) / σ
x : the value being solved for
μ : the average or mean
σ : the standard deviation
Sample z-score problem
Haley received a 92 on a test. The class average is 76 with a standard deviation of 7. What is the z-score?
z = (92 - 76) / 7
The z-score is: 2.2857
What does this mean?
This value means that Haley's 92 is 2.2857 standard deviations from the mean. If she fell within 2 standard deviations to the right and left of the average score she would have been within 95% of the class scores, but because she is slightly over 2 standard deviations, it can be inferred that she did better than 95% of the class.