Originally Posted by
Pride
In a setting with students and test grades, the teacher adds up all the scores and divides by the number of students. What's the difference between this and what your average is?
The difference is, is that instead of dividing by the number of people participating, he is suggesting that they instead, divide by the number of submissions.
For example, let's say 6 people submitted 13 items, all with scores of 7. If we divided by the number of people, we would get a final score of 13*7/6, which is 15.167, a disproportionately high number (as the highest score possible is a 10). If, in another case, 6 people submitted 20 items with scores of 5, we would have a final score of 20*5/6. That's 16.67; here, we would have the number of people contributing work being the same, but they did more work, and got a higher score for it.
The problem with having outrageously high scores above 10 can be solved by dividing by the number of submissions, instead of number of participants. The primary problem is that people can submit more than one item. By removing the number of participants from the bottom of the equation, we should have a more realistic and fair statistic. In the case that we have 7 participants, each one of them submitting 10 items, all with scores of 9, we instead have (7*10*9)/(7*10); final score of 9, which is less than 10. If the total number of submissions is limited to 10, then the equation turns out to become 10*9/10 (which is 9), the total score divided by the number of submissions.
By dividing the total score by submissions and not participants, we should have a mathematically reasonable answer, remove the gender participation disparity, and therefore, have a more successful event. Although to be perfectly fair, AK was the only one here using the correct version of an "average." The assumption you've taken dividing by the number of students in your example, is that each student could only submit one item, thus making the number of tests and students to be the same value.
In summary, AK is entirely correct in this situation and you all (that means
all of you) owe him an apology, and we should be dividing by submissions into the total score.