Question for the Math heads

[swanniez1983]

There is currently a competition at my partner's work (mobile phone store) to win a plasma screen TV plus surround sound system. This is a nationwide competition. Basically, all the stores are divided up into one of either three groups, based on how "busy" they are in terms of how many contracts the store sells per week 1) Busy 10+ 2) Moderate 6-10 3) Quiet 1-5. Now, each store from each group is set a "target" number of contract sales per week. The competition lasts for 9 weeks and they aim to sell as many contracts as they can during this period. The store from each group which has sold the greatest % above their set target, wins the plasma screen + surround system.

So, my partner's store is in the "quiet" group and the target is 5. There are other stores with a target as low as 1. After one week, my partner's store sold 10 contracts, making it 200% of the store's target. Say one of the stores with a target of 1 sold 2 contracts, again making it 200% of the store's target. However, my partner thinks this calculation is unfair as it's much easier for the store with a target of one to sell two contracts(making it 200%) than it would be for my partner's store to sell an extra 5, above the 5 already required to break even, to give the same 200%. I hope this makes sense! Anyways, is there a way to somehow weight the % to take into account the differences in targets between stores? They have kinda done this by dividing all the stores into three groups, but it still seems a bit unfair....

 

[daddy_4_eyes]

When dealing with a number that small I don't think you can weight it appropriately.

But as an idea, find their sales figures for the past x-months and find how many of their weeks falls outside 2 standard deviations of their mean contract sales. You might see how spread out their weekly contract sales are. If there's a lot of outliers (sp??) you might find their mean contract sales to be misleading and thus their target to be unfair.

That said, you'd have to compare it to other stores as well as the cumulative performance of all the stores to see if their results are uncommon in any way.

 

[swanniez1983]

My partner showed me the current leaderboard based on sales over the last two weeks. What they have done is to determine the current % of the final target after the 9 week period i.e partner's store target is 45 contracts over 9 weeks (5 a week x 9 weeks). Partner's store sold 23 contracts over the last two weeks. Therefore, her current store's % after two weeks is ~51% of the final target (23/45).

Another store is on ~56%, but their target over 9 weeks is only 18. They have sold 10 contracts over two weeks (6 above their target after two weeks) --> 10/18 = ~56% of final target. On the otherhand, partner's store has sold 13 contracts above their two week target, but her store's % is less.

Oh, and just to add, the top store from EACH group wins a plasma screen + surround sound system