Values based on multiple percentages

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Nesuke

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Oct 18, 2013
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Hi,

I have a task to work out values based on a number of different variables. The total number is 5000 but here is the stipulations:

40% Male, 60% Female
then 20% under 25, 60% 25-50 and 40% over 50
then 30% have an income of 10k-20k, 40% have an income of 20k-30k and 30% an income of 40k+

As you can see, I need to work out values where they "cross over" each of these variables so that the total of each is true to the overall total. Is there any formula or way I can easily work this out rather than having to go through each variable manually working it out?

Thanks.
 
Nesuke said:
I have a task to work out values based on a number of different variables.
Click to expand...
You have to "work out" the "values" of what? Based on which variables that stand for what?

Nesuke said:
The total number is 5000 but here is the stipulations:
Click to expand...
The "total number" of what?

Nesuke said:
40% Male, 60% Female
then 20% under 25, 60% 25-50 and 40% over 50
then 30% have an income of 10k-20k, 40% have an income of 20k-30k and 30% an income of 40k+
Click to expand...
What is meant by "then"? Are you working with conditional probabilities in some manner?

Nesuke said:
As you can see, I need to work out values where they "cross over" each of these variables so that the total of each is true to the overall total.
Click to expand...
What should we be "seeing"? What is the "they"? What is meant by "crossing over"? The "total" of what? So what is "true"? Of the overall total of what?

Please reply with the full and exact text of the exercise, the complete instructions, and a clear listing of your thoughts and efforts so far, including whatever rules, formulas, theorems, etc, you believe you may be expected to apply to this exercise. Thank you. ;)
 
Well I'll put it to you as an example. I need 100 cats, 40 of them need to be Male, 60 need to be Female. But then 30 of them need to be black, 40 need stripes and 30 need to be patchy. Then even on top of that 70 need to have long hair and then 30 need to have short hair.

So basically I need to work out how many cats I need that are Male, Black, Long Haired. Male, Striped, Long Haired. Male, Patchy, Long Haired. etc etc. I think you get the idea (this isn't the real exercise by the way if you're thinking I'm some kind of mad cat man).

I just wanted to know if there's any formula or method that can work this out rather than having to manually re-iterate through each probability. Sometimes this could be layered 5 or 6 times, so the amount of values could stretch into four figures, so you can understand why I would like to cut down on manual time.
 
Nesuke said:
Well I'll put it to you as an example. I need 100 cats, 40 of them need to be Male, 60 need to be Female. But then 30 of them need to be black, 40 need stripes and 30 need to be patchy. Then even on top of that 70 need to have long hair and then 30 need to have short hair.

So basically I need to work out how many cats I need that are Male, Black, Long Haired. Male, Striped, Long Haired. Male, Patchy, Long Haired. etc etc....
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As currently posted, I don't think this has a unique solution. The exact text of the exercise would be helpful. ;)
 
Nesuke said:
Well I'll put it to you as an example. I need 100 cats, 40 of them need to be Male, 60 need to be Female. But then 30 of them need to be black, 40 need stripes and 30 need to be patchy. Then even on top of that 70 need to have long hair and then 30 need to have short hair.

So basically I need to work out how many cats I need that are Male, Black, Long Haired. Male, Striped, Long Haired. Male, Patchy, Long Haired. etc etc. I think you get the idea (this isn't the real exercise by the way if you're thinking I'm some kind of mad cat man).

I just wanted to know if there's any formula or method that can work this out rather than having to manually re-iterate through each probability. Sometimes this could be layered 5 or 6 times, so the amount of values could stretch into four figures, so you can understand why I would like to cut down on manual time.
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Do you know a programming language? This appears to me to be a matter of determining how many cells you have in an n-dimensional matrix and then populating them so that the "marginal" totals come out right. I doubt there is a formula, and I doubt that there will usually be a single correct way to populate. I suspect, however, there is an algorithm that will give you a correct population.
 
Nesuke said:
Hi,

I have a task to work out values based on a number of different variables. The total number is 5000 but here is the stipulations:

40% Male, 60% Female
then 20% under 25, 60% 25-50 and 40% over 50
then 30% have an income of 10k-20k, 40% have an income of 20k-30k and 30% an income of 40k+

As you can see, I need to work out values where they "cross over" each of these variables so that the total of each is true to the overall total. Is there any formula or way I can easily work this out rather than having to go through each variable manually working it out?

Thanks.
Click to expand...
To write your data on a flat piece of paper, you will have to make three charts. The first I would make with columns for male & female, and 3 rows for the age categories. [A third column and a 4th row give the sums across and down.] Then a second chart could have rows for salary groups instead of age, while the third would be age vs. salary.

An alternate way would have the same first sheet, which represents the sum over all salaries. On top of that build three more layers for the three salary groups. No problem making multi-dimensional tables in a computer, a little harder on paper!
 
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