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I'm not sure the correct term for my problem is weighted average. But let me explain.

I've conducted a survey where participants answer on a scale betweeen $1$ and $7$. The questions fall into three categories. In category one & two there are $12$ questions, and in category three there are four questions.

Lets assume there are nine participants and the distribution of the answers are $579$ points in category one. $450$ points in category two and $87$ in category three.

I want to calculate/show the answer distribution of each category (compared to the total points), taking into account that category three is three times smaller.

I hope I'm making sense.

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The question is not clear to me. Certainly, you can say the average answer on category 1 is $579/108$ (the 108 comes from $9\times12$, on category 2, $450/108$, and on category 3, $87/36$. But I think you are asking for more than that. – Gerry Myerson May 24 '13 at 10:37
@GerryMyerson: let me try again: The current numbers give a false indication of the actual points contribution for each category, towards the total. Category 1 and 2 are evenly matched, but the 3rd. category only has 36 questions (vs. 108). So the score of 87 wont work, when I try to show, as a percentage, how many points each category contributed. - well that wasn't any clearer. – JacobSDK May 24 '13 at 10:48
up vote 0 down vote accepted

Just multiply the points in third category by 3 to make points in different categories comparable. BTW There is a separate forum for Statistics Cross Validated

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Thank you, I did that, but wasn't sure if I then had to add the multiplied points (271) to the total. – JacobSDK May 24 '13 at 10:56
I think you'll find that $3\times 87\ne271$. But, more to the point, you didn't say anything in your question about wanting to add the points from the different categories together. For what reason do you want to do that? – Gerry Myerson May 24 '13 at 11:01
@GerryMyerson to get the answer distribution in %. Thank you for your help. – JacobSDK May 24 '13 at 11:15
I don't know what "to get the answer distribution in percent" means. – Gerry Myerson May 24 '13 at 11:39
So the % will be (579/(579+450+261))*100=44.88,(450/(579+450+261))*100=34.88 & (261/(579+450+261))*100=20.23. If I have understood your requirement correctly. – Wishwas May 24 '13 at 12:44

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