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Let $\mathbb{F}_q$ denote a finite field of odd cardinality $q$,$\mathbb{A}=\mathbb{F}_q[T]$ the polynomial ring over $\mathbb{F}_q$ and$k=\mathbb{F}_q(T)$ the rational function field over $\mathbb{F}_q$. In thispaper, we compute the average value of the size of the group$K_2(\mathcal{O}_{\gamma D})$, where $\mathcal{O}_{\gamma D}$ denotes theintegral closure of $\mathbb{A}$ in $k(\sqrt{\gamma D})$, $D$ is a monic,square-free polynomial of even degree and $\gamma$ is a fixed generator of$\mathbb{F}_q^*$.

Remark on a Simple Proof of the Mean Value of $K_2(\mathcal{O})$ in Function Fields