# Average per line vs. Average per column: is total average the same?

I'm a student in humanities---maths aren't my strong points, but I'm trying hard, so bear with me please:

I have a survey with seven questions (A to G) and a population divided in four categories (1 to 4). The answer to each question may be True or False.

First, I made a calculation of the total of true answers per person and calculated the average of True answer per person per category (i.e. Total of True answers per line for each individual of a given category, divided by the total number of people for that category).

Second, I calculated the total of True answers per question and calculated their respective index of True answers (i.e. Total of True answers per column for each individual of a given category divided by the total number of people for that category). I expect the total of the 7 indices per category to provide the average of True answers in that category.

But it happens that my two results differ, so either I am really confused or I made a mistake somewhere. Could you help me clear this up? Thanks.

I've tried to put together a simplified example:

     A B C D E F G   T
1.  0 1 0 1 0 0 1   3
2.  1 0 0 1 0 1 0   3
3.  1 0 0 1 0 0 0   2
4.  0 0 0 0 1 0 0   1
5.  1 0 1 0 0 0 0   2

T   3 1 1 3 1 1 1  11


Total population: Tp = 5
Total questions: Tq = 7
Total correct answers: Tc = 11
Total of correct answers for question A: TA = 3
Index of correct answers to question A: (iA) = TA / Tp

And here is where the confusion reigns:
Average of correct answer per person: = Tc / Tp =? iA+iB+iC+iD+iE+iF+iG

Now that I write it down again, it should be correct, shouldn't it? If so I must have made a mistake on my spreadsheet, which is worth another question in itself.

• I find the "index" part a bit confusing, and it seems like you can (for the sake of the question) drop the whole category business. The question would benefit by a small example. – Karl Aug 22 '11 at 12:08
• By index I mean part/whole. I don't know how I can put an example in there, but I will try. – Benjamin Aug 22 '11 at 12:13
• You could add a little table typeset by a monospace font, using the code button which looks like "{ }". – Karl Aug 22 '11 at 12:35
• I did add an example, I hope it makes sense. Thanks. – Benjamin Aug 22 '11 at 13:31