Z Score
Calculator
Results
- Z-score
- 2
- Deviation from the mean
- 30
Statistical results
| Z-score | 2 |
| Deviation from the mean | 30 |
formula-map diagram
- Z-score
- 2
- Deviation from the mean
- 30
Statistical relationship
Formula
z = (x − μ) / σ= 2
Note
This is a simplified model: it applies the displayed standard formula to the summary values you entered and assumes their underlying conditions (independence, normality, correct sampling) hold. It does not analyse a real data set. Check the assumptions before relying on the result.
More in Statistics and probability
See all →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 of its distribution. A z-score of 0 means the value equals the mean, positive values are above it, and negative values are below it.
How is the z-score formula derived?+
It's calculated as (value − mean) / standard deviation. Subtracting the mean centers the data at zero, and dividing by the standard deviation rescales it so distances are measured in standard-deviation units rather than the original units.
What counts as an unusually high or low z-score?+
In a roughly normal distribution, about 68% of values fall within z = ±1, 95% within ±2, and 99.7% within ±3. A z-score beyond ±2 or ±3 is generally considered unusual or an outlier.
Can I compare z-scores from two different data sets?+
Yes, that's one of the main uses of standardization. Because z-scores remove the original units and scale, a z-score of 1.5 on a test means the same relative standing regardless of what the underlying measurement was.
Does the z-score assume a normal distribution?+
The calculation itself works for any distribution, but the common interpretation using the 68-95-99.7 rule only holds precisely when the underlying data is approximately normally distributed. For skewed data, the z-score is still valid as a standardized distance, just not as a probability estimate.