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Default Pivot Table - Weight Average

I have a situation that requires the need for weight averaged subtotals and
totals. I have no options but to use Pivot Tables for what I am trying to
accomplish. I record coal train data for 25 different contracts and need the
ability to show weight averaged coal qualities in my subtotals by differing
contracts. I have been using pivot tables to track customer information for a
long time and it works perfectly except for the fact that I now need to be
able to weight average some of the information based on the tonnage for each
train which varies significantly. I am somewhat familiar with calculated
fields but the weight average needs to happen at a subtotal based on all of
the coal shipped to individual contracts. Reality would be 25 differing
contracts with 4-5 trains per day to continuously update. All of the
weighting would occur on the tonnage. The list is constantly growing as the
year passes so I need the flexibility of a pivot table vs. hard formulas in a
worksheet. Here is a basic example of what I am trying to do.
Train#1 (15000tons 9500 BTU)
Train#2 (14500tons 9200 BTU)
Train#3 (15150tons 9350 BTU)
Need the weight average BTU
To complicate this matter, the I have no option of changing reports
therefore I need to make this work using pivot tables
Please HELP!!!!!!!!!!

 
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