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Default Need to average division of two columns based on criteria

I have two sheets
Sheet 1 contains Catagories with respective beginning and ending values (Ie
Category A begins at 10 and ends at 20) There are about 75 categories all
with different beginning and ending values. There is no overlapping, so no
category can contain the same number.
Category CPT Range Start End
E&M Office Visits 99201 - 99215 99201 99215
E&M Hospital Services 99217 - 99239 99217 99239
E&M Consultations 99241 - 99255 99241 99255
E&M Neonatal 99295 - 99300 99295 99300

Sheet 2 contains all the numbers that correspond to the 75 categories (Ie 10
- 10000) in column A. Column B contains an "amount" for each number and
column C contains another "amount" for each number.

Column A Column B Column C
99201 35 40
99202 40 45
99203 45 50
99204 50 55

What i am trying to do is return the average of the range for a category
when dividing one amount by another amount. So for Category E&M Office
Visits i would want to return the average of column c/column b for all codes
within the range (99201-99215). Can this be done without using a macro??

For further information (Column A in Sheet 2 Contains 16,0000 numbers
ranging from 10000 to 99999)
 
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