Bell curve grading normalizes raw scores using z-scores: z = (raw - class_mean) / class_SD, then rescales to a target distribution: curved = z * target_SD + target_mean. If your class averaged 65% with SD 15, and you want a 75% average with SD 10, a student scoring 80% gets z = 1.0, curved = 85%.
- Step 1: Calculate z-score for each student's raw score
- Step 2: Rescale using target mean and target SD
- Step 3: Apply standard grade cutoffs (A >= 90, B >= 80, etc.)
- Preserves relative ranking while shifting the distribution
- Class mean moves to exactly the target mean
| Raw Score | Z-Score (mean 65, SD 15) | Curved (target 75, SD 10) | Grade |
|---|---|---|---|
| 45% | -1.33 | 61.7% | D- |
| 65% | 0.00 | 75.0% | C |
| 80% | +1.00 | 85.0% | B |
| 95% | +2.00 | 95.0% | A |