Test Score Analyzer
Analyze where your test score falls relative to the class using mean and standard deviation to compute z-score and percentile.
Results
Visualization
How It Works
A z-score tells you how many standard deviations your score is above or below the class average. This is the foundation of grading on a curve and lets you compare performance across different tests with different scales. A z-score of 0 means you scored exactly at the mean; +1 means one standard deviation above.
The Formula
Variables
- X — Your individual test score
- mu — Class mean (average score)
- sigma — Class standard deviation (spread of scores)
- z — Z-score: number of standard deviations from the mean
Worked Example
You score 82 on a test where the class mean is 75 and the standard deviation is 10. Your z-score is (82 - 75) / 10 = 0.70, which corresponds to approximately the 76th percentile. You scored better than about 76% of the class.
Practical Tips
- A z-score between -1 and +1 covers about 68% of all students — this is the 'average' range.
- A z-score above +2 puts you in the top 2.3% of the class — an exceptional performance.
- Standard deviation measures how spread out the scores are. A small SD means everyone scored similarly.
- If you don't know the class SD, a typical value for a college exam is 10-15 points on a 100-point scale.
- Professors who 'curve' grades are typically mapping z-scores to letter grades using cutoffs like this calculator shows.
Frequently Asked Questions
What is a good z-score on a test?
A z-score of +1.0 or higher is generally good, placing you in approximately the 84th percentile. A z-score of +2.0 (97.7th percentile) is excellent. A z-score of 0 means you scored exactly at the class average.
How is grading on a curve different from straight grading?
Straight grading uses fixed cutoffs (e.g., 90+ = A). Curved grading assigns grades based on relative performance: your z-score determines your grade regardless of the raw score, which compensates for unusually hard or easy tests.
Can my z-score be negative?
Yes. A negative z-score means you scored below the class mean. For example, a z-score of -1.0 means you scored one standard deviation below average, placing you around the 16th percentile.
Why does the standard deviation matter?
The standard deviation determines how 'impressive' your distance from the mean is. Scoring 10 points above average is more significant when the SD is 5 (z = 2.0) than when the SD is 20 (z = 0.5).
Is the percentile the same as my grade percentage?
No. Percentile tells you what percentage of students you outperformed. A 75th percentile does not mean you got 75% correct — it means you scored better than 75% of the class.