How to calculate weighted means when determining individual contribution to a goal

Question

Not sure if I worded the question right. And I'm not particularly sure if I know the terms I am looking for.

Please help me understand this better.

I have a group of students who participate together in a fundraising event. The money raised will be divided up and distributed to each student's individual account based on two things:

1. The percentage each age group is in the overall number of students who participated
2. The "value" each age group brings to the event.

I have 3 age groups. Groups 1, 2 and 3. Not all age groups will necessarily participate. If an equal number of students from each age group participates then Group 1 will earn 1/6 of the total, Group 2 will earn 1/3 of the total, and Group 3 will earn 1/2 of the total.

Example: 1 student from each age group participates in a fundraiser and raises $300 The student from Group 1 will be given $50. The student from Group 2 will be given $100. The student from Group 3 will be given $150.

What is it called, and how do I calculate out different scenarios, like:

• 3 students from Group 3, and 1 student from Group 2 participates in a fundraiser and raised $400
• 3 students from Group 3, 3 students from Group 2, and 1 student from Group 1 participates in a fundraiser and raises $300

Is there a general formula for this?

Thanks in advance!

Answer 1

I just had to step away and think about this in simpler terms. I was trying to group each student in to an age group then determine their level of contribution to the overall goal as a group. Really, I just needed to determine each student's contribution individually after assigning an individual weight to their contribution.

Very simply: StudentPortion = TotalMoneyRaised * StudentWeight / TotalWeight

Where StudentPortion is the amount of money earned by a student and TotalWeight is the combined weight of all students.

If age group 1 has a weight of .167, age group 2 has a weight of .333, and age group 3 has a weight of .5 and we have 2 students in each age group and a total amount of $500 raised, then each student in age group 1 earns 500 * .167 / 1.5 dollars.

Funny that I took a simple ratio and made it so complicated.