Krdytkyu

UPDATE (with specific questions q1-q3)

Welcome any pointers on how to weigh 2 variables: num_privateschools and num_privatepupils in a state.

Would I do the following to combine (weigh) them so that $500k sales data gets distributed according to both these variables:

((%numprivateshools + %numprivatepupils)/2)*$500k ?

So the combined factor for each state would be

A: ((.12+.12)/2)*$500k (where 12% of private schools and 12% of private students are in State A)

B: ((.23+.29)/2)*$500k

C: ((.18+.18)/2)*$500k

D: ((.47+.41)/2)*$500k

But isn't this just a simple average?

Q1: can I simply add the percentages from the variables even though they are on different scales (pupils vs schools)?

Q2: it seems that I'm not really "weighing" the two variables differently since we are simply adding them (and so weighing them equally?). What am I missing? Is there a way to add a weight to each variable based on my data or does this weight variable come from subject knowledge?

Q3: could I use num_privatepupils as a weight for num_private schools? If so would I simply multiply them
Rather than add? For state B, would It be correct to do .21(.23)*$500k ?

Thanks for your help in advance

Some more details on the data:

here is some data for 6 variables:

State:student_population:num_private_schools:num_public_schools:num_pupils_privateschool:num_pupils_publicschools

A:100k:10:500:200:14000

B:90k:20:350:500:10000

C:125k:15:450:300:9500

D:300k:40:900:700:20000

And here is a national sales number: $500k

I want to distribute the $500k to the state level using the variables above.

I could distribute the national data according to the "distribution" (the percentage in each state) of each of these variables individually, like so:

State:%student_population:%num_private_schools:%num-public_schools

A:.16:.12:.23

B:.15:.23:.16

C:.20:.18:.20

D:.49:.47:.41

So for state A, 16% of sales would be assigned based on the population data, 12% based on number of private schools in the state, and 23% based on the public schools variable (similarly for the other states). The point is each variable will distribute the 500k differently (500k*%student_population will be differently distributed than 500k*%private_schools).

But what I want is to distribute the data according to some weights. So my question is: How can I combine these variables so that my national data (the $500k) is distributed according to a combined factor of these various variables?