Average Coupon Savings

[jerryroxas]

Hello! I was wondering if anyone could help me figure out an equation?

Here's the problem I have:

• I offered 5 coupons to a group of 10 people. The coupons are good for discounts of $5, $4, $3, $2 & $1 respectively. The 10 people had the choice to use all, some or none of the coupons. Obviously, I can calculate what the average savings per person was by doing the following: (# used * coupon value)/10.
• However, what I'd really like to know is what was the weighted average savings achieved per persons who utilized coupons?
• For example, out of the 10 people, if coupon utilization was 3-people-used-$5-coupon, 5-people-used-$4-coupon, 7-people-used-$3-coupon, 6-people-used-$2-coupon and 4-people-used-$1-coupon, what was the weighted average savings for 7 people (max 7 people used $3 coupon)??
• And should the weighted average savings be calculated for 7 people?? Since, technically, 7 unique people used the $3 coupon, and the remaining 3 people could have used the $5, meaning all 10 people used coupons....

Here's what I'm trying to calculate:

• If I give you a book of these 5 coupons, I want to be able to tell you how much you will likely save on average, using the empirical data above. My terminology may be wrong, but I'm thinking its going to be a weighted average calculation, since there is a higher probability of people using the $3 coupon than there is of people using the $1 coupon.

I tried doing a weighted average calculation, but doesn't seem to get me where I need to go. Am I just confused?? Any help and/or clarification would be much appreciated!

Thanks!

 

[stapel]

Are they all coupons for the same thing? Is that thing commonly used? In which case, wouldn't people generally use all of the coupons, starting with the highest in value?

 

[jerryroxas]

Are they all coupons for the same thing? Is that thing commonly used? In which case, wouldn't people generally use all of the coupons, starting with the highest in value?

no, the coupons are for different things. for example, the $3 coupon might be for gas (something that everyone uses) and the $4 coupon might be for a ladies manicure, in which case only women would use it (assuming that the coupons cannot be given away and use by people who did not receive the coupon book directly)). therefore the $3 coupon would have a higher weight than the $4 coupon for people who receive the coupon book.

 

[stapel]

no, the coupons are for different things.

Then I don't think there's any way, other than by taking a fairly huge but granular sample, to predict, estimate, or average what "people" are going to do. There are just way too many variables. Sorry.

 

[jerryroxas]

Then I don't think there's any way, other than by taking a fairly huge but granular sample, to predict, estimate, or average what "people" are going to do. There are just way too many variables. Sorry.

no worries, thanks for taking a look at it! what if i had a larger sample, say of 1000 people?

 

[stapel]

no worries, thanks for taking a look at it! what if i had a larger sample, say of 1000 people?

How granular is your data? For instance, how specific is your information for gender (male, female, otherwise), SE status (wealthy, lower-middle class, etc), marital status (never married, divorced, etc), employment (full-time, stay-at-home, etc), time of the year or type of prevailing weather (could any of your coupons be perceived as "seasonal"?), type of residential area (rural, gentrified, etc), region (Deep South, Nunavut, etc), and other types of specifications? How many hundreds or thousands of data points do you have for each?