Z-Score Calculator
Calculate z-scores to determine how many standard deviations a value is from the mean. Essential for statistics, standardized testing, and data analysis.
Z-Score Results
| # | Value | Z-Score | Interpretation |
|---|
Interpreting Z-Scores
z > 2
Significantly above average (top 2.5%)
1 < z ≤ 2
Above average
-1 ≤ z ≤ 1
Around average (68% of data)
z < -2
Significantly below average (bottom 2.5%)
Formula:
z = (x - μ) / σ
Where: x = value, μ (mu) = mean, σ (sigma) = standard deviation
Understanding Z-Scores
What is a Z-Score?
A z-score (also called standard score) indicates how many standard deviations a value is from the mean. Positive z-scores are above the mean, negative z-scores are below the mean, and z = 0 means the value equals the mean.
When to Use Z-Scores
- Comparing values from different datasets or scales
- z
- Standardized test score interpretation (SAT, IQ, etc.)
- Quality control and process monitoring
- Determining percentiles and probabilities
Real-World Example
If test scores have a mean of 75 and standard deviation of 10, a score of 85 would have z = (85 - 75) / 10 = 1.0, meaning it's 1 standard deviation above average (better than approximately 84% of test takers).
Common Mistakes
- Using sample standard deviation when population standard deviation is needed
- Applying z-scores to non-normal distributions without caution
- Confusing z-score with percentile (they're related but different)
Educational Purpose Disclaimer
This calculator is provided for educational purposes only. Results should not be used as the sole basis for critical decisions. Always verify important calculations independently and consult qualified professionals when needed.