# Thread: ***Fun Challenge -- weighted average of global rankings***

1. ## ***Fun Challenge -- weighted average of global rankings***

Goal
The goal is to create a weighted average of global rankings. Does not have to be perfectly accurate (if that was even possible).

Specific Example
To make this problem less abstract and easier, we are going to use a specific example -- Sweden. Sweden is ranked by the following numbers:

2 overall
8.67 index score

http://en.wikipedia.org/wiki/Global_...-2011_rankings
2 overall
5.56 index score

On http://en.wikipedia.org/wiki/Global_...nked_countries
10 overall
1.56 index score

Expanded Goal
1 -- Now we don't want to use the "overall" rank because the "separation" between each overall rank are not "equal."
1a -- Doing this will lead to less accuracy in the combined ranking.

2 -- Instead, what we want to do is "factor" in the index score onto the overall rank.
2a -- The index score can be seen as a % or a proportion out of 100.
2b -- Using this new "factored number," a combined ranking can be made.

The Problem
How do you create a weighted average that is based off of (or at least accounts for) the index scores?

The "standard" or "common" weighted average is basically the following method: ((a% * a) + (b% * b) + (c% * c))/3
So we can call the mentioned problem and goal a "factored average" instead of a "weighted average" as the terms may cause unnecessary confusion, unless there is already a phrase/label for specifically the mentioned problem and goal.

Next step -- Solution
There may be need for clarification, and I'll try my best to make something more specific, but I'm pretty sure a leading statistician can easily understand, and solve the problem, just as easily.

***Please do not use specific statistical terminologies unless you feel they are absolutely necessary. If a poster uses any terms outside of the language used in this post, feel free to explain them as soon as they are used (or link to a clear, concise explanation).

You should be able to explain the solution to a junior high school girl. If you cannot, then the solution is neither clear nor concise.

2. ## Re: ***Fun Challenge -- weighted average of global rankings***

See http://www.physicsforums.com/showthr...29#post3418429 for clarification if it may help.

3. ## Re: ***Fun Challenge -- weighted average of global rankings***

Well, this may sound like "specific statistical terminology" but I think you want to create one single index based on these three different scores. Although a weighted average may be a solution, the weighting you use will be subjective. Perhaps using Principal Components Analysis you can create an index that resumes the three measures giving an equal weight to the three measures:

http://www.statisticspedia.com/artic...step-by-step1/

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