In a 'more than' cumulative frequency table, the ordinary frequency of a class is obtained by:

A 'more than' entry counts every observation at or above that boundary, so the entries DECREASE. 'more than 200' minus 'more than 300' leaves exactly the observations lying in 200-300, so $f$ = current entry − next entry. Subtracting the PREVIOUS entry is the rule for a 'less than' table, where the entries increase instead. Adding two entries gives a number larger than $n$, and dividing by the number of classes has no meaning here. Only after this conversion can you build the ordinary cumulative column that $\frac{n}{2}$ is compared against.