Combining Percentages
The data on 4 examinations showed scores of 75 percent correct, 87 percent correct, 69 percent correct, and 93 percent correct. The overall grade was determined by taking the Arithmetic Mean (or 'average') of these scores, reporting a combined percentage of 81.
Consider that the 4 examinations had
24 correct out 32 questions for 75 percent
87 correct out of 100 questions for 87 percent
38 correct out of 55 questions for 69 percent
and 93 correct out of 100 questions for 93 percent.
Thus if the questions are of equal merit across the examinations, there are 242 questions answered correctly out of 287 for a percentage of 84.3.
Discuss the discrepancy between 81 percent and 84.3 percent for these two computations.
What is the mathematical explanation?
Another example:
30 correct out 32 questions for 94 percent
75 correct out of 100 questions for 75 percent
50 correct out of 55 questions for 91 percent
and 69 correct out of 100 questions for 69 percent.
Here, the AM = 82.3 percent whereas 224 correct out of 287 is 78 percent.
