That's an interesting question, but we cannot really say whether "average" is a noun, verb or adjective in the sentence, because as you can see, it is not really a full sentence!
It could be used as a noun :
The average is 200m. OR They have an average of 200m.
It could be used as a verb:
They average 200m.
But it would be a little strange or illogical if it was used as an adjective:
An average 200m.
Normally the average is calculated from many different numbers, and if they are ALL exactly 200m, the average would always be 200m and we would not use the word at all.
In the same way, it would not be logical to talk about a long 200m or a short 200m.
It might be an interesting 200m, or an exciting 200m but an average 200m just sounds like the 200m is not too boring!