Hmmm, I think that a way to solve these kind of problems is to look at them this way:
If you take the average of (26 + 324)/2, you will get an average of 175
Then, you take the next pair of even integers at both extremes: (28 + 322)/2 and you will also get 175, you do this all the way until you get to the pair of integers in the center of the set: (174 + 176)/2 = 175. Hence, the answer resides in understanding that the average of all the numbers in the set is simply the spread of the extreme numbers ( ie 26 and 324) divided by 2. Hope I was clear enough.