Estimation — moments and likelihood for a shifted uniform

Let $X_1,X_2,…,X_n$ $(n\ge2)$ be a random sample from Uniform$\left[-\frac{3\theta}{2},\frac{\theta}{2}\right]$ distribution, where $\theta>0$ is an unknown parameter. Let $\bar X$, $X_{(1)}$ and $X_{(n)}$ denote respectively the mean, the smallest order statistic and the largest order statistic of the sample. Then which of the following statements are true?