Z-Score Calculator
Find how many standard deviations a value sits from the mean.
Z-score1.5000
The z-score is z = (x − μ) ÷ σ — the number of standard deviations a value lies above (positive) or below (negative) the mean. With x = 85, a mean of 70 and a standard deviation of 10, z = (85 − 70) ÷ 10 = 1.5, so 85 is one and a half standard deviations above average. A z-score of 0 means the value equals the mean.
Questions
How do I calculate a z-score?
Subtract the mean from your value, then divide by the standard deviation: z = (x − μ) ÷ σ. A value of 85 with a mean of 70 and a standard deviation of 10 gives z = (85 − 70) ÷ 10 = 1.5.
What does a negative z-score mean?
A negative z-score means the value is below the mean; a positive one means it is above. The size tells you how far: a z of −2 is two standard deviations below average.
What is a typical range for z-scores?
For roughly bell-shaped data, about 95% of values fall between z = −2 and z = +2, and almost all between −3 and +3. Values beyond ±3 are unusual.