Applied math problem: library collection development
First of all, this is my first post here. I struggled with forum selection. If there is a more appropriate forum, I hope mods will assist me in moving the thread.
I am using "relative use" to determine a "demand" variable to assist me in allocating my library materials budget between various component collections.
u = number of times books are picked up or "used" for each component collection
v = number of volumes, or books, in a component collection
U = total number of uses for all component collections
V = total number of volumes in all component collections
r = relative use, or (u/v)/(U/V)
d = demand, or (u*r) for each component collection.
The problem is that it is not behaving how I would expect: the sum total of the demands of all component collections does not equal the demand for the entire collection as a whole. Where is my math going wrong, if this expectation is correct?
Here are my numbers (space delimited, please tell me if there is a better way to display this). I've been using a spreadsheet for this.
Collection u v r d
Fiction 15716 8818 1.13 17765
LP Fiction 948 725 0.83 786
Mystery 6150 3822 1.02 6276
LP Mystery 220 219 0.64 140
SciFi 1639 1704 0.61 1000
SS 358 403 0.56 202
Western 458 475 0.61 280
Total Demand: 25,489
Sum of component Demands: 26,449
Shouldn't these be the same?