Hello, all. I put this question in the statistics forum because I believe it fits best here.
Could someone please explain to me the steps I would have to take to solve the following problem? To be clear, I'm not looking for an answer to the problem, but just the steps I must take to solve it correctly.
Of 150 customers who were eligible to receive a reward for their patronage, 85 customers received 5 different kinds of rewards, each with a different value (i.e., reward 1 was worth so many points, reward 2 was worth so many points, etc.) The value of the rewards increases with reward type and when combined, yielded a weighted reward rate of 101.8%. I'm assuming that because the weighted reward rate is not higher, more lower value rewards were distributed than higher value ones. What I need to determine is exactly how many of each kind of reward was given to each of the 85 customers (for example, 15 customers got reward 1, 20 got reward 2, etc.)
What I've done so far:
Because I'm terrible at this, I assumed that as long as my calculations equaled 101.8%, I had reached the right answer. I set up an excel sheet that is designed to determine weighted averages in test scores and came up with this:
REWARD PERCENT WEIGHT CONTRIBUTION
Level One .982 .1 .0982
Level Two .018 .2 .018
When you add the two contribution figures you get .1018. Converted to a percentage, this equals 101.8%.
I thought I was on the right track doing this but my wife suggested that I had not accounted for all of the levels. With that in mind, two additional questions: am I indeed on the right track, and would one be correct in saying that because the weighted reward rate is low, more lower valued rewards were distributed? Any help is enormously valuable and appreciated!