MHB Help Solve This Financial Puzzle: Dropping Rebates Per Case

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The discussion centers on analyzing a drop in overall rebates per case from £16.30 to £15.96, resulting in a financial impact of £13,566. The user seeks to break down this total by ingredient to identify how changes in the number of cases ordered, particularly for soft drinks, contribute to the overall decline. Suggestions include calculating weighted averages to apportion the rebate changes by product. The importance of understanding both the rebate per case and the number of cases ordered is emphasized in explaining the financial shifts. The goal is to clarify the specific drivers behind the rebate changes for better financial insights.
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Hi,

I'm trying to prove something that I think is simple but am really struggling so would greatly appreciate any help!

Over 2 weeks I receive rebates, the value of the rebate can vary both due to the rebate on each case and also the number of cases ordered.
Between week 25 and week 26 my overall rebate per case dropped from £16.30 to £15.96 which has a financial impact of 13,566. I know this is the right number as it takes into account variation on rebate per case and the number of cases ordered but it is the same calculation in the individual ingredient rows above but they don't add up to this total.

Basically I want to prove how to split the 13,656 by ingredient to for example show that even though our rebate per case on soft drinks increased, because we have ordered 308 less cases this is causing our overall rebate per case to decline so that I can say how much of the 13,656 drop is driven by this.

The numbers are in the JPG file attached and would really value some clever brains to help me solve the riddle.

Thanks!

Hannah
 

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hannahg252 said:
Hi,

I'm trying to prove something that I think is simple but am really struggling so would greatly appreciate any help!

Over 2 weeks I receive rebates, the value of the rebate can vary both due to the rebate on each case and also the number of cases ordered.
Between week 25 and week 26 my overall rebate per case dropped from £16.30 to £15.96 which has a financial impact of 13,566. I know this is the right number as it takes into account variation on rebate per case and the number of cases ordered but it is the same calculation in the individual ingredient rows above but they don't add up to this total.

Basically I want to prove how to split the 13,656 by ingredient to for example show that even though our rebate per case on soft drinks increased, because we have ordered 308 less cases this is causing our overall rebate per case to decline so that I can say how much of the 13,656 drop is driven by this.

The numbers are in the JPG file attached and would really value some clever brains to help me solve the riddle.

Thanks!

Hannah

In this particular case you can say the change in the amount of rebates was caused totally by the change in the rebates in soft drinks [just look at the differences by product]. As an explanation of why this is true, you can point to the change in the number of each product.

Generally, when trying to apportion results by product, one computes percentages (that is weighted averages). Thus one could, if it made sense otherwise, compute the percentage of the total of your last column and apply that to the 13,566. Once again, this might tell you what, but not why.
 
I have been insisting to my statistics students that for probabilities, the rule is the number of significant figures is the number of digits past the leading zeros or leading nines. For example to give 4 significant figures for a probability: 0.000001234 and 0.99999991234 are the correct number of decimal places. That way the complementary probability can also be given to the same significant figures ( 0.999998766 and 0.00000008766 respectively). More generally if you have a value that...

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