A dataset $X$ consisting of $n \ge 3$ elements has a mean $\bar{x}$ and a sample variance $s^2$. If we construct a new dataset $Y$ by replacing the maximum element $x_{\max}$ and the minimum element $x_{\min}$ with their arithmetic mean $m = \frac{x_{\max} + x_{\min}}{2}$, how does the new sample variance $s_Y^2$ relate to $s^2$?