differences when calculating averages?

I'm helping my wife analyse some data from a university experiment, and I've used the AVERAGEIFS function. But I can't quite get the results to match up when I tried checking the results. Let me describe what I've done:

I've got a worksheet with 2857 rows of data which came from 28 participants. Here is one of the formula's I created for averaging response time for each participant in this experiment:

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The "101" and "102" are participant numbers.

At the end I entered this formula to get an overall average of all the response times, I obviously have no criteria for participant number here, but other than that the criteria are the same:

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Just as a quick test I did an average of all the individual results like this, The cells B2 to B29 contain the above formula:
=AVERAGE(B2:B29)

I would have expected the same result, but I don't! Using the AVERAGEIFS function to get an overall average I get 1146.007485. Using the AVERAGE function on the individual AVERAGEIFS results I get 1147.61511, a difference of 1.6. A huge difference when I had expected no difference. And in one of the other calculations the difference between the two functions is 3.6. What is going on here, am I doing something wrong, and if so, what? I have manually calculated the results for one of the participants, and my results are the same as the AVERAGEIFS formula used for that individual participant.

An average of averages isn't always a good measure.

Let's say we have two participants in a study, who have been asked to rate two factors on a scale of 1-3

The first participant answer 1 & 3 = an average of 2
The second participant answers 3 and N/A = an average of 3

The average of their averages is (2+3)/2 = 2.5, but the average of all of the answers given is (1+3+3)/3 = 2.3'

The 'correct' average is the average of all of the answers, not the average of the average - so in your example the AVERAGEIFS will be giving the correct answer and the AVERAGE(B2:B29) is misleading you.