Individual Summed doesn't equal combined? WHY?

[steevsaul]

Hi Everyone,

Noone I know can give a mathematical reason why the below problem exists. I will explain what the parameters are and what we see happening and if anyone can solve the problem then that will be impressive..

The problem is about putting a waterfall chart together where individual inputs are changed and their overall effect on the final number are apportioned.

NRV (Net rock volume) is the product of GRV (Gross Rock Volume) and NTG (Net to Gross).

There are two zones (A and B) which have different starting (OLD) and NEW GRV and NTG and therefore NRV numbers.

Looking at Zone A the new NRV is 825 (product of 1500 and 0.55). The proportion of the change (325) attributable to GRV is 250 (calculated by ((1500-1000)/1000)*500) which is the percentage increase in GRV multiplied by the original NRV. Doing the same calculation for NTG gives 75 as the change in NRV attributable to NTG. Adding the two together gives 325 which ties out with the total change in NRV.

Now to the main problem. When we do this individually for each zone we get the first numbers in the image highlighted in yellow. A total change in NRV of 345 (245 from GRV change and 100 from NTG change)..

HOWEVER, when we sum the GRV of the two zones together we get 1300 OLD and 1750 NEW which is a change of 450 (matches). The NRV change is still 345 however the proportion using the same maths attributable to GRV is now 183 (((1750-1300)/1300)*530)..

Can anyone tell me why there is a difference when we look at the sum of the individual zones versus the combined zones.

Thanks,
SteveView attachment 5449

 

[jvicens]

Hi Steve,

I can certainly understand your confusion about the discrepancy in the NRV change when looking at the individual zones versus the combined zones. This is actually a common issue in mathematical analysis and can be explained by the concept of proportionality.

In your calculation for the proportion of change attributable to GRV, you are using the original NRV value of 500. However, when you combine the two zones, the original NRV value is no longer 500, but rather 530. This means that the proportion of change attributable to GRV should also be recalculated using the new NRV value of 530.

Using the updated NRV value, the proportion of change attributable to GRV for the combined zones would be 183, which matches the total NRV change of 345. This is because the change in GRV for the combined zones is actually larger than the individual zones, resulting in a higher proportion of change for GRV.

I hope this explanation helps to clear up the confusion and solve the problem you were facing. If you have any further questions, please don't hesitate to ask.