What is the distribution of grade points in a class of 200 with the class average of 3.70?

Question

The incoming class of 200 at xyz medical school has a class average GPA of 3.70. What is the distribution of grades ( GPAs ) on a 4 point scale to get the average 3.70

Answer 1

We need to know the spread of the data to determine the grading. The spread is indicated by the standard deviation from the mean. The mean is insufficient to show the spread. If the distribution is normal, the grading can be in quartiles. Grade D could be the lowest 0-25% quartile; C is 25% to 50%; B is 50% to 75%; and above 75% is A. So if 3.7 is the average GPA, we can determine the quartiles. If we use Z-scores then Z_D≤-0.6745, -0.6745≤Z_C≤0, 0≤Z_B≤0.6745, Z_A≥0.6745.

To find out the GPA (variable X), (X-3.7)/s=Z-score values shown above. Since we don't know s we can't actually do the calculations. When we know s we can find the relevant GPA values by solving for X.

This is my interpretation of the question, and how I think the answer can be worked out.