For starters this line is wrong, a list can not be even:
(if (even? lst)
A list's length, however, is a different matter:
(if (even? (length lst))
Also, in both procedures the comparison for determining if the list's mid point has been reached is wrong, you'll have to tweak this line in both helper procedures, because currently is not working:
(if (= times_carred ...
It'll be simpler if you start times_carred
in 1
and change the condition to (>= times_carred (/ (length lst) 2))
, the same comparison works for both cases.