Grade Curve worksheet

1. Curved class average: 73.78

1. Average the original scores

   $\frac{72+65+58+\text{…}+70}{10}$$=71.8$

2. Points to add: the target average minus the current average

   $74-71.8$$=2.2$

3. Add those points to every score, keeping each between 0 and 100. For the first score

   $72+2.2$$=74.2$

4. Average the curved scores to get the new class average

   $\frac{74.2+67.2+60.2+\text{…}+72.2}{10}$$=73.78$

2. Curved class average: 85.61

1. Take the square root of each score and multiply by 10. This lifts low scores most and keeps 100 at 100. For the first score

   $10\times \sqrt{52}$$=72.111026$

2. Average the curved scores to get the new class average

   $\frac{72.111026+78.102497+82.462113+\text{…}+93.808315}{10}$$=85.610457$

3. Curved class average: 83.48

1. Average the original scores

   $\frac{42+78+45+\text{…}+70}{10}$$=69.8$

2. Points to add: the target average minus the current average

   $85-69.8$$=15.2$

3. Add those points to every score, keeping each between 0 and 100. For the first score

   $42+15.2$$=57.2$

4. Average the curved scores to get the new class average

   $\frac{57.2+93.2+60.2+\text{…}+85.2}{10}$$=83.48$

4. Curved class average: 75.7

1. Find the highest score and the points needed to raise it to the target

   $90-88$$=2$

2. Add those points to every score, so the gaps between students stay the same. For the first score

   $52+2$$=54$

3. Average the curved scores to get the new class average

   $\frac{54+63+70+\text{…}+90}{10}$$=75.7$

5. Curved class average: 82.65

1. Take the square root of each score and multiply by 10. This lifts low scores most and keeps 100 at 100. For the first score

   $10\times \sqrt{46}$$=67.8233$

2. Average the curved scores to get the new class average

   $\frac{67.8233+74.833148+77.459667+\text{…}+100}{10}$$=82.650698$

6. Curved class average: 80.25

1. Average the original scores

   $\frac{60+60+45+\text{…}+90}{10}$$=74.5$

2. Points to add: the target average minus the current average

   $82-74.5$$=7.5$

3. Add those points to every score, keeping each between 0 and 100. For the first score

   $60+7.5$$=67.5$

4. Average the curved scores to get the new class average

   $\frac{67.5+67.5+52.5+\text{…}+97.5}{10}$$=80.25$

7. Curved class average: 60

1. Average the original scores

   $\frac{48+45+60+\text{…}+90}{10}$$=77.4$

2. Points to add: the target average minus the current average

   $60-77.4$$=\mathrm{-17.4}$

3. Add those points to every score, keeping each between 0 and 100. For the first score

   $48+\left(\mathrm{-17.4}\right)$$=30.6$

4. Average the curved scores to get the new class average

   $\frac{30.6+27.6+42.6+\text{…}+72.6}{10}$$=60$

8. Curved class average: 98.78

1. Average the original scores

   $\frac{42+54+56+\text{…}+69}{10}$$=64.1$

2. Points to add: the target average minus the current average

   $110-64.1$$=45.9$

3. Add those points to every score, keeping each between 0 and 100. For the first score

   $42+45.9$$=87.9$

4. Average the curved scores to get the new class average

   $\frac{87.9+99.9+100+\text{…}+100}{10}$$=98.78$

9. Curved class average: 75

1. Average the original scores

   $\frac{47+74+85+\text{…}+78}{10}$$=75.9$

2. Find the standard deviation (SD), the typical distance from the average. Square each score's distance from the average, average those, then take the square root

   $\sqrt{\frac{\mathrm{2,210.9}}{10}}$$=14.869095$

3. Place each score the same number of SDs from the new average as it was from the old one, kept between 0 and 100. For the first score

   $75+11\times \frac{47-75.9}{14.869095}$$=53.620085$

4. Average the curved scores to get the new class average

   $\frac{53.620085+73.5944+81.732084+\text{…}+76.553558}{10}$$=75$

10. Curved class average: 65

1. Average the original scores

   $\frac{52+61+68+\text{…}+88}{10}$$=73.7$

2. Find the standard deviation (SD), the typical distance from the average. Square each score's distance from the average, average those, then take the square root

   $\sqrt{\frac{\mathrm{1,136.1}}{10}}$$=10.658799$

3. Place each score the same number of SDs from the new average as it was from the old one, kept between 0 and 100. For the first score

   $65+10\times \frac{52-73.7}{10.658799}$$=44.641234$

4. Average the curved scores to get the new class average

   $\frac{44.641234+53.084962+59.652306+\text{…}+78.416145}{10}$$=65$