I would like to know the difference between two approaches of combining percentages.
I found an online example that match my situation; the example have been found in The University of Georgia page. It states:
"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.
75 + 87 + 69 + 93 / 4 = 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."
I have similar situation on my research, and there is a difference between the percentages. I would like to understand the difference between these two computation.
Best Answer
The difference is that the first average regards each test as having equal weight, while the second average regards each question as having equal weight.
If it really doesn't matter how many questions are on a test, then the first average is better.
If it really doesn't matter how the question pool is divided up into tests, then the second average is better.
Long story short, neither is more correct without additional context.