What is the meaning of "shoot the average"?
Solution 1:
I think the author is saying they were significantly younger or older than the rest of their group.
The appropriate definition from Collins is:
no longer working or effective: "It's no good - these gears are shot."
That is, the author was so much younger (or older) than the rest of the group that they "broke" the average (but not the median, so they must mean "mean").