Let $x=\{11,12,13, \ldots, 40,41\}$ and $Y=\{61,62,63, \ldots, 90,91\}$ be the two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and $\sigma^2$ is the variance of all the observations in $X \cup Y$, then $\left|\overline{\mathrm{x}}+\overline{\mathrm{y}}-\sigma^2\right|$ is equal to $\_\_\_\_$ .