$\color{olive}{F = A_1 \oplus A_2 \dots \oplus A_{n-1} \oplus A_n}$ is true if it contains odd number of $1's$, which makes me say $\color{olive}{A \oplus B \oplus C \oplus D}$ is correct answer. But let's also see the other way
Question says function contains half of minterms (means $8$ minterms), with odd number of $1's$. Some minterms would be $\overline{A}BCD$, $ABC\overline{D}$, and so on. K-MAP looks like $\Rightarrow$
$\color{blue}{F(A,B,C,D) = \sum (1,2,4,7,8,11,13,14) = A \oplus B \oplus C \oplus D}$