Dear all I'm looking for some help and confirmation since it's been a while since I have done these types of calculations.
I'm trying to calculate a few things with regards to populations. I want to have them weigthed on 2 or maybe 3 types of criteria, such as life expectancy, percentage of total population, amount of income, and maybe some other factors.
Normally with only 1 criteria/weight I know how to do this and it would be fairly easy.
By example for life expectancy, I could sum the life expectancy of each age group I take, giving me a total amount of life expectancy over all the age groups. I could then divide the value of each age group by the total give me a percentage or fraction of 1.
Basically $\sum_{i=0}^n (w_i \cdot x_i)$ or $\frac{\sum_{i=0}^n (v_i \cdot x_i)}{\sum_{i=0}^n v_i}$
However this is only for 1 criteria. If I start multiplying fractions (percentages) I won't get the right number and only smaller and smaller fractions not adding up to unity.
This for 2 weights would then be incorrect $\sum_{i=0}^n (w_1i \cdot w_2i \cdot x_i)$ With w being the weighted fractions.
What would be the best way to handle this and are there any "standard/common" equations or methods for this?
Unfortunately my first Google searches and math stack exchange didn't show me any useful results. (Keep in mind I might not have searched using the correct terms as it has been a while)